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Posts
Full color printing!
Published:
3D Printing of Invariant Manifolds in Dynamical Systems
Published:
The following paper appeared: Patrick R. Bishop, Summer Chenoweth, Emmanuel Fleurantin, Alonso Ogueda-Oliva, Evelyn Sander, and Julia Seay, 3D Printing of Invariant Manifolds in Dynamical Systems, AMS Notices, 73(1): 5-15 (2026), doi:10.1090/noti3288, 2026.
Stability of Floating Objects at a Two-Fluid Interface
Published:
GMU Math Makerlab members published a paper:
Mathematics of Floating 3D Printed Objects
Published:
Members of the GMU Math Makerlab published a paper:
3D Printing Data
Published:
3D printing is a great way to represent data. Here are a couple of examples created by students.
Topographic Maps
Published:
Sugihara Cylinders
Published:
Modeling Dynamical Systems for 3D Printing
Published:
Iterated Function Systems
Published:
In Fall 2021, GMU Math 401, Mathematics Through 3D Printing, created iterated function systems.
House Street Pentagon Tiling
Published:
GMU Figure Eight Knot
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portfolio
publications
Geometry Forum articles
Published in Geometry Center, University of Minnesota, 1994
Citation: Evelyn Sander, Geometry Forum articles, Geometry Center, University of Minnesota, Report GCG69, 1994.
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Fractals and fractal correlations
Published in Computers in Physics, 1994
Citation: Evelyn Sander, Leonard M. Sander, and Robert M. Ziff, Fractals and fractal correlations, Computers in Physics, 8(4):420-425, 1994.
Further Geometry Forum Articles
Published in Geometry Center, University of Minnesota, 1995
Citation: Robert Hesse and Evelyn Sander, Further Geometry Forum Articles, Geometry Center, University of Minnesota, Report GCG83, 1995.
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Hyperbolic Sets for Noninvertible Maps and Relations
Published in PhD Thesis, 1996
Citation: Evelyn Sander, Hyperbolic Sets for Noninvertible Maps and Relations, PhD Thesis, University of Minnesota, 1996.
A new proof of the stable manifold theorem
Published in Zeitschrift für angewandte Mathematik und Physik (ZAMP), 1996
Citation: Evelyn Sander and Richard McGehee, A new proof of the stable manifold theorem, Zeitschrift für angewandte Mathematik und Physik (ZAMP), 47:497-513, 1996.
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Hyperbolic sets for noninvertible maps and relations
Published in Discrete and Continuous Dynamical Systems- Series A, 1999
Citation: Evelyn Sander, Hyperbolic sets for noninvertible maps and relations, Discrete and Continuous Dynamical Systems- Series A, 5(2):339-358, 1999.
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Monte Carlo simulations for spinodal decomposition
Published in Journal of Statistical Physics, 1999
Citation: Evelyn Sander and Thomas Wanner, Monte Carlo simulations for spinodal decomposition, Journal of Statistical Physics, 95(5-6):925-948, 1999.
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Homoclinic tangles for noninvertible maps
Published in Nonlinear Analysis, 2000
Citation: Evelyn Sander, Homoclinic tangles for noninvertible maps, Nonlinear Analysis, 41(1-2):259-276, 2000.
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Spinodal decomposition: A survey of recent results
Published in International Conference on Differential Equations, 2000
Citation: Stanislaus Maier-Paape, Evelyn Sander, and Thomas Wanner, Spinodal decomposition: A survey of recent results, International Conference on Differential Equations, 2:1288-1299, 2000.
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Unexpectedly Linear Behavior for the Cahn–Hilliard Equation
Published in SIAM Journal on Applied Mathematics, 2000
Citation: Evelyn Sander and Thomas Wanner, Unexpectedly Linear Behavior for the Cahn–Hilliard Equation, SIAM Journal on Applied Mathematics, 60(6):2182-2202, 2000.
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Against All Odds: Review of Women Becoming Mathematicians by Margaret Murray
Published in American Scientist, 2001
Citation: Evelyn Sander, Against All Odds: Review of Women Becoming Mathematicians by Margaret Murray, American Scientist, January-February, 2001.
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Explosions: Global Bifurcations at Heteroclinic Tangencies
Published in Ergodic Theory and Dynamical Systems, 2002
Citation: Kathleen T. Alligood, Evelyn Sander, and James A. Yorke, Explosions: Global Bifurcations at Heteroclinic Tangencies, Ergodic Theory and Dynamical Systems, 22(4):953-972, 2002.
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Limits to the experimental detection of nonlinear synchrony
Published in Physical Review E, 2002
Citation: Paul So, Ernest Barreto, Krešimir Josić, Evelyn Sander, and Steven J. Schiff, Limits to the experimental detection of nonlinear synchrony, Physical Review E, 65(4):046225, 2002.
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The geometry of chaos synchronization
Published in Chaos, 2003
Citation: Ernest Barreto, Krešimir Josić, Carlos J. Morales*, Evelyn Sander, and Paul So, The geometry of chaos synchronization, Chaos, 13(1):151-164, 2003.
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Pattern formation in a nonlinear model for animal coats
Published in Journal of Differential Equations, 2003
Citation: Evelyn Sander and Thomas Wanner, Pattern formation in a nonlinear model for animal coats, Journal of Differential Equations, 191(1):143-174, 2003.
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The structure of synchronization sets for noninvertible systems
Published in Chaos, 2004
Citation: Krešimir Josić and Evelyn Sander, The structure of synchronization sets for noninvertible systems, Chaos, 14(2):249-262, 2004.
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A description of the DSWeb Tutorials Competition
Published in Dynamical Systems Magazine, 2005
Citation: Evelyn Sander, A description of the DSWeb Tutorials Competition, Dynamical Systems Magazine, July, 2005.
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Dynamics of noninvertibility in delay equations
Published in Discrete and Continuous Dynamical Systems, 2005
Citation: Ernest Barreto, Evelyn Sander, Steven J. Schiff, and Paul So, Dynamics of noninvertibility in delay equations, Discrete and Continuous Dynamical Systems, 768-777, 2005.
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Three-dimensional crisis: Crossing bifurcations and unstable dimension variability
Published in Phys. Rev. Lett., 2006
Citation: Kathleen T. Alligood, Evelyn Sander, and James A. Yorke, Three-dimensional crisis: Crossing bifurcations and unstable dimension variability, Phys. Rev. Lett., 96(24):244103, 2006.
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Complex transient patterns on the disk
Published in Discrete and Continuous Dynamical Systems, Series A, 2006
Citation: Jonathan P. Desi*, Evelyn Sander, and Thomas Wanner, Complex transient patterns on the disk, Discrete and Continuous Dynamical Systems, Series A, 15(4):1049-1078, 2006.
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Explosions in dimensions one through three
Published in Rendiconti del Seminario Matematico, Torino, 2007
Citation: Kathleen T. Alligood, Evelyn Sander, and James A. Yorke, Explosions in dimensions one through three, Rendiconti del Seminario Matematico, Torino, 65(1): 1-15, 2007.
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Noninvertibility
Published in Scholarpedia, 2009
Citation: Ernest Barreto, Paul So, and Evelyn Sander, Noninvertibility, Scholarpedia, 4(8):2242, 2009.
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A classification of explosions in dimension one
Published in Ergodic Theory and Dynamical Systems, 2009
Citation: Evelyn Sander and James A. Yorke, A classification of explosions in dimension one, Ergodic Theory and Dynamical Systems, 29: 715-731, 2009.
Journal Link | Alternate link | arXiv
Period-doubling cascades for large perturbations of Henon families
Published in Journal of Fixed Point Theory and Applications, 2009
Citation: Evelyn Sander and James A. Yorke, Period-doubling cascades for large perturbations of Henon families, Journal of Fixed Point Theory and Applications, 6(1): 153-163, 2009.
Journal Link | Alternate link | arXiv
Fixed points indices and period-doubling cascades
Published in Journal of Fixed Point Theory and Applications, 2010
Citation: Madhura R. Joglekar†, Evelyn Sander, and James A. Yorke, Fixed points indices and period-doubling cascades, Journal of Fixed Point Theory and Applications, 8(1):151-176, 2010.
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The dynamics of nucleation in stochastic Cahn-Morral systems
Published in SIAM Journal on Applied Dynamical Systems, 2011
Citation: Jonathan P. Desi†, Hanein Edrees*, Joseph J. Price*, Evelyn Sander, and Thomas Wanner, The dynamics of nucleation in stochastic Cahn-Morral systems, SIAM Journal on Applied Dynamical Systems, 10(2): 707-743, 2011.
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The Dynamical Systems Track at ICIAM 2011 in Vancouver
Published in Dynamical Systems Magazine, 2011
Citation: Evelyn Sander, The Dynamical Systems Track at ICIAM 2011 in Vancouver, Dynamical Systems Magazine, October, 2011.
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Period-doubling cascades galore
Published in Ergodic Theory and Dynamical Systems, 2011
Citation: Evelyn Sander and James A. Yorke, Period-doubling cascades galore, Ergodic Theory and Dynamical Systems, 31(4):1249-1267, 2011.
Journal Link | Alternate link | arXiv
Connecting period-doubling cascades to chaos
Published in International Journal of Bifurcation and Chaos, 2012
Citation: Evelyn Sander and James A. Yorke, Connecting period-doubling cascades to chaos, International Journal of Bifurcation and Chaos, 22 (2): 1250022-1, 2012.
Journal Link | arXiv
Pattern formation in a mixed local and nonlocal reaction-diffusion system
Published in Electronic Journal of Differential Equations, 2012
Citation: Richard Tatum† and Evelyn Sander, Pattern formation in a mixed local and nonlocal reaction-diffusion system, Electronic Journal of Differential Equations, 160: 1-30, 2012.
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Branch interactions and long-term dynamics for the diblock copolymer model in one dimension
Published in Discrete and Continuous Dynamical Systems- Series A, 2013
Citation: Ian Johnson*, Evelyn Sander, and Thomas Wanner, Branch interactions and long-term dynamics for the diblock copolymer model in one dimension, Discrete and Continuous Dynamical Systems- Series A, 33(8): 3671 - 3705, 2013.
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A period-doubling cascade precedes chaos for planar maps
Published in Chaos, 2013
Citation: Evelyn Sander and James A. Yorke, A period-doubling cascade precedes chaos for planar maps, Chaos, 23(3): 033113, 2013.
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GMU Math MakerLab
Published in Blog , 2014
The zombie swarm: Epidemics in the presence of social attraction and repulsion
Published in Mathematical Modelling of Zombies (R. Smith?, editor), 2014
Citation: Evelyn Sander and Chad M. Topaz, The zombie swarm: Epidemics in the presence of social attraction and repulsion, Mathematical Modelling of Zombies (R. Smith?, editor), University of Ottawa Press, 265-300, 2014.
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The many facets of chaos
Published in International Journal of Bifurcation and Chaos, 2015
Citation: Evelyn Sander and James A. Yorke, The many facets of chaos, International Journal of Bifurcation and Chaos, 25(4): 1530011, 2015.
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Chaos and its manifestations
Published in SIAM News, 2015
Citation: Evelyn Sander and James A. Yorke, Chaos and its manifestations, SIAM News, 48(7) September, 2015.
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Degenerate Nucleation in the Cahn–Hilliard–Cook Model
Published in SIAM Journal on Applied Dynamical Systems, 2016
Citation: Dirk Blömker, Evelyn Sander, and Thomas Wanner, Degenerate Nucleation in the Cahn–Hilliard–Cook Model, SIAM Journal on Applied Dynamical Systems, 15(1): 459-494, doi:10.1137/15M1028844, 2016.
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Measuring quasiperiodicity
Published in Europhysics Letters, 2016
Citation: Suddhasattwa Das†, Chris B. Dock*, Yoshitaka Saiki, Martin Salgado-Flores*, Evelyn Sander, Jin Wu*, and James A. Yorke, Measuring quasiperiodicity, Europhysics Letters, 114(4):40005, 2016.
Journal Link | Alternate link | arXiv
Quasiperiodicity: Rotation numbers
Published in Proceedings of The Foundations of Chaos Revisited: From Poincaré to Recent Advancements, 2016
Citation: Suddhasattwa Das†, Yoshitaka Saiki, Evelyn Sander, and James A. Yorke, Quasiperiodicity: Rotation numbers, Proceedings of The Foundations of Chaos Revisited: From Poincaré to Recent Advancements, Chapter 7, 103-118, Springer Complexity, Switzerland, 2016.
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Effects of polarization induced by non-weak electric fields on the excitability of elongated neurons with active dendrites
Published in Journal of Computational Neuroscience, 2016
Citation: Robert I. Reznik†, Ernest Barreto, Evelyn Sander, and Paul So, Effects of polarization induced by non-weak electric fields on the excitability of elongated neurons with active dendrites, Journal of Computational Neuroscience, 40(1): 27-50, 2016.
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Validated Saddle-Node Bifurcations and Applications to Lattice Dynamical Systems
Published in SIAM Journal on Applied Dynamical Systems, 2016
Citation: Evelyn Sander and Thomas Wanner, Validated Saddle-Node Bifurcations and Applications to Lattice Dynamical Systems, SIAM Journal on Applied Dynamical Systems, 15(3): 1690-1733, 2016.
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Quantitative quasiperiodicity
Published in Nonlinearity, 2017
Citation: Suddhasattwa Das†, Yoshitaka Saiki, Evelyn Sander, and James A. Yorke, Quantitative quasiperiodicity, Nonlinearity, 30(11): 4111-4140, 2017.
Journal Link | Alternate link | arXiv
Rigorous continuation of bifurcation points in the diblock copolymer equation
Published in Journal of Computational Dynamics, 2017
Citation: Jean-Philippe Lessard, Evelyn Sander, and Thomas Wanner, Rigorous continuation of bifurcation points in the diblock copolymer equation, Journal of Computational Dynamics, 4(1&2):71-118, 2017.
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Generalized Lorenz equations on a three-sphere
Published in The European Physical Journal Special Topics, 2017
Citation: Yoshitaka Saiki, Evelyn Sander, and James A. Yorke, Generalized Lorenz equations on a three-sphere, The European Physical Journal Special Topics, 226 (9) 1751-1764, 2017.
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Solving the Babylonian Problem of quasiperiodic rotation rates
Published in Discrete & Continuous Dynamical Systems - S, 2019
Citation: Suddhasattwa Das†, Yoshitaka Saiki, Evelyn Sander, and James A. Yorke, Solving the Babylonian Problem of quasiperiodic rotation rates, Discrete & Continuous Dynamical Systems - S, 12(8): 2279-2305, 2019.
Journal Link | Alternate link | arXiv
Margaret Beck, Crawford Prizewinner
Published in Dynamical Systems Magazine, 2019
Citation: Evelyn Sander, Margaret Beck, Crawford Prizewinner, Dynamical Systems Magazine, July, 2019.
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An entry in the 3D Printing section
Published in Illustrating Mathematics, 2020
Citation: Evelyn Sander (Edited by Diana Davis), An entry in the 3D Printing section, Illustrating Mathematics, American Mathematical Society, 2020.
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Modeling Dynamical Systems for 3D Printing
Published in AMS Notices, 2020
Citation: Stephen K. Lucas, Evelyn Sander, and Laura Taalman, Modeling Dynamical Systems for 3D Printing, AMS Notices, 67(11): 1692-1705 (2020), doi:10.1090/noti2187, 2020.
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Birkhoff Averages and Rotational Invariant Circles for Area-Preserving Maps
Published in Physica D, 2020
Citation: Evelyn Sander and James D. Meiss, Birkhoff Averages and Rotational Invariant Circles for Area-Preserving Maps, Physica D, 411: 132569 (2020), doi:10.1016/j.physd.2020.132569, 2020.
Journal Link | Alternate link | arXiv
Graduate Assistants supporting active learning in graduate classrooms
Published in On Demand, Innovations in Teaching & Learning Conference Proceedings, 2021
Citation: Rebecca R.G., Hannah Klawa†, Cigole Thomas†, Long Nguyen†, Joanna G. Jauchen, Padmanabhan Seshaiyer, and Evelyn Sander, Graduate Assistants supporting active learning in graduate classrooms, On Demand, Innovations in Teaching & Learning Conference Proceedings, 13 (2021), doi:10.13021/itlcp.2021.3007, 2021.
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Birkhoff Averages and the Breakdown of Invariant Tori in Volume-Preserving Maps
Published in Physica D, 2021
Citation: Evelyn Sander and James D. Meiss, Birkhoff Averages and the Breakdown of Invariant Tori in Volume-Preserving Maps, Physica D, 428: 133048 (2021), doi:10.1016/j.physd.2021.133048, 2021.
Journal Link | Alternate link | arXiv
Equilibrium Validation in Models for Pattern Formation Based on Sobolev Embeddings
Published in Discrete and Continuous Dynamical Systems Series B, 2021
Citation: Evelyn Sander and Thomas Wanner, Equilibrium Validation in Models for Pattern Formation Based on Sobolev Embeddings, Discrete and Continuous Dynamical Systems Series B, 26(1): 603-632, doi:10.3934/dcdsb.2020260, 2021.
Journal Link | arXiv
A Computer-Assisted Study of Red Coral Population Dynamics
Published in Pure and Applied Functional Analysis, 2022
Citation: Sayomi Kamimoto†, Hye Kyung Kim*, Evelyn Sander, and Thomas Wanner, A Computer-Assisted Study of Red Coral Population Dynamics, Pure and Applied Functional Analysis, 7(4): 1307-1337 (2022), 2022.
Journal Link | arXiv
Modeling Dynamical Systems for 3D Printing
Published in The Best Writing on Mathematics 2021, 2022
Citation: Stephen K. Lucas, Evelyn Sander, and Laura Taalman (Edited by Mircea Pitici), Modeling Dynamical Systems for 3D Printing, The Best Writing on Mathematics 2021, Princeton University Press, 2022.
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Equilibrium validation for triblock copolymers via inverse norm bounds for fourth-order elliptic operators
Published in Communications in Nonlinear Science and Numerical Simulation, 2022
Citation: Peter Rizzi†, Evelyn Sander, and Thomas Wanner, Equilibrium validation for triblock copolymers via inverse norm bounds for fourth-order elliptic operators, Communications in Nonlinear Science and Numerical Simulation, 115: 106789 (2022), doi:10.1016/j.cnsns.2022.106789, 2022.
Journal Link | arXiv
Mathematics of Floating 3D Printed Objects
Published in Proceedings of Symposia in Applied Mathematics (PSAPM), 2023
Citation: Daniel M. Anderson, Brandon G. Barreto-Rosa*, Joshua D. Calvano*, Lujain Nsair*, and Evelyn Sander, Mathematics of Floating 3D Printed Objects, Proceedings of Symposia in Applied Mathematics (PSAPM), 79: 19-50, edited by Maria Trnkova and Andrew Yarmola, American Mathematical Society (2023), doi:10.1090/psapm/079/00710, 2023.
Journal Link | arXiv
GLAMS: Graduate Learning Assistants in Mathematical Sciences
Published in Problems, Resources, and Issues in Mathematics Undergraduate Studies (PRIMUS), 2023
Citation: Joanna G. Jauchen, Hannah Klawa†, Long Nguyen†, Rebecca R.G., Evelyn Sander, Padmanabhan Seshaiyer, and Cigole Thomas†, GLAMS: Graduate Learning Assistants in Mathematical Sciences, Problems, Resources, and Issues in Mathematics Undergraduate Studies (PRIMUS), 33(8): 819-840 (2023), doi:10.1080/10511970.2023.2172751, 2023.
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Reliability and robustness of oscillations in some slow-fast chaotic systems
Published in Chaos, 2023
Citation: Jonathan Jaquette, Sonal Kedia, Evelyn Sander, and Jonathan Touboul, Reliability and robustness of oscillations in some slow-fast chaotic systems, Chaos, 33, 103135 (2023), doi:10.1063/5.0166846, 2023.
Journal Link | arXiv
Cyclic Symmetry Induced Pitchfork Bifurcations in the Diblock Copolymer Model
Published in Discrete and Continuous Dynamical Systems Series B, 2024
Citation: Peter Rizzi†, Evelyn Sander, and Thomas Wanner, Cyclic Symmetry Induced Pitchfork Bifurcations in the Diblock Copolymer Model, Discrete and Continuous Dynamical Systems Series B, 29(2): 666-701 (2024), doi:10.3934/dcdsb.2023109, 2024.
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Stability of Floating Objects at a Two-Fluid Interface
Published in European Journal of Physics , 2024
Citation: Daniel M. Anderson, Patrick R. Bishop†, Mark Brant*, Gabriela Castaneda Guzman*, Evelyn Sander, and Gina Thomas*, Stability of Floating Objects at a Two-Fluid Interface, European Journal of Physics, 45: 055001 (2024), doi:10.1088/1361-6404/ad5ca8, 2024.
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Proportions of Incommensurate, Resonant, and Chaotic Orbits for Torus Maps
Published in Chaos: An Interdisciplinary Journal of Nonlinear Science (AIP), 2025
Citation: Evelyn Sander and James D. Meiss, Proportions of Incommensurate, Resonant, and Chaotic Orbits for Torus Maps, Chaos: An Interdisciplinary Journal of Nonlinear Science (AIP), 35, 013147 (2025), doi:10.1063/5.0226617, 2025.
Journal Link | arXiv
Resonance and Weak Chaos in Quasiperiodically-Forced Circle Maps
Published in Communications in Nonlinear Science and Numerical Simulation, 2025
Citation: James D. Meiss and Evelyn Sander, Resonance and Weak Chaos in Quasiperiodically-Forced Circle Maps, Communications in Nonlinear Science and Numerical Simulation, 142: 108562, 2025.
Journal Link | arXiv
Computing Lyapunov Exponents using Weighted Birkhoff Averages
Published in Journal of Physics A: Mathematical and Theoretical, 2025
Citation: Evelyn Sander and James D. Meiss, Computing Lyapunov Exponents using Weighted Birkhoff Averages, Journal of Physics A: Mathematical and Theoretical, 58(2025):355701, doi:10.1088/1751-8121/adfac1, 2025.
Journal Link | arXiv
Dynamics of Perturbed Elliptical Billiard Tables
Submitted, 2026
Citation: Patrick R. Bishop†, Summer Chenoweth†, Emmanuel Fleurantin, Jay Mireles James, and Evelyn Sander, Dynamics of Perturbed Elliptical Billiard Tables, Submitted, 2026.
arXiv
3D Printing of Invariant Manifolds in Dynamical Systems
Published in AMS Notices, 2026
Citation: Patrick R. Bishop†, Summer Chenoweth†, Emmanuel Fleurantin, Alonso Ogueda-Oliva†, Evelyn Sander, and Julia Seay†, 3D Printing of Invariant Manifolds in Dynamical Systems, AMS Notices, 73(1):5-15 (2026), doi:10.1090/noti3288, 2026.
Journal Link | arXiv
Validation of Symmetry Induced Bifurcation Points in Nonlinear Diffusion Problems
Submitted, 2026
Citation: Maxime Breden, Evelyn Sander, and Thomas Wanner, Validation of Symmetry Induced Bifurcation Points in Nonlinear Diffusion Problems, Submitted, 2026.
arXiv