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On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards
1. | Department of Mathematics, Penn State University, University Park, PA 16802, United States, United States |
[1] |
Lucas Dahinden, Álvaro del Pino. Introducing sub-Riemannian and sub-Finsler billiards. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022014 |
[2] |
Erlend Grong, Alexander Vasil’ev. Sub-Riemannian and sub-Lorentzian geometry on $SU(1,1)$ and on its universal cover. Journal of Geometric Mechanics, 2011, 3 (2) : 225-260. doi: 10.3934/jgm.2011.3.225 |
[3] |
Yunlong Huang, P. S. Krishnaprasad. Sub-Riemannian geometry and finite time thermodynamics Part 1: The stochastic oscillator. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : 1243-1268. doi: 10.3934/dcdss.2020072 |
[4] |
Stefan Sommer, Anne Marie Svane. Modelling anisotropic covariance using stochastic development and sub-Riemannian frame bundle geometry. Journal of Geometric Mechanics, 2017, 9 (3) : 391-410. doi: 10.3934/jgm.2017015 |
[5] |
Nicolas Dirr, Federica Dragoni, Max von Renesse. Evolution by mean curvature flow in sub-Riemannian geometries: A stochastic approach. Communications on Pure and Applied Analysis, 2010, 9 (2) : 307-326. doi: 10.3934/cpaa.2010.9.307 |
[6] |
Richard Evan Schwartz. Outer billiards and the pinwheel map. Journal of Modern Dynamics, 2011, 5 (2) : 255-283. doi: 10.3934/jmd.2011.5.255 |
[7] |
Paul W. Y. Lee, Chengbo Li, Igor Zelenko. Ricci curvature type lower bounds for sub-Riemannian structures on Sasakian manifolds. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 303-321. doi: 10.3934/dcds.2016.36.303 |
[8] |
Beatrice Abbondanza, Stefano Biagi. Riesz-type representation formulas for subharmonic functions in sub-Riemannian settings. Communications on Pure and Applied Analysis, 2021, 20 (9) : 3161-3192. doi: 10.3934/cpaa.2021101 |
[9] |
Richard Evan Schwartz. Unbounded orbits for outer billiards I. Journal of Modern Dynamics, 2007, 1 (3) : 371-424. doi: 10.3934/jmd.2007.1.371 |
[10] |
Daniel Genin. Research announcement: Boundedness of orbits for trapezoidal outer billiards. Electronic Research Announcements, 2008, 15: 71-78. doi: 10.3934/era.2008.15.71 |
[11] |
Richard Evan Schwartz. Research announcement: unbounded orbits for outer billiards. Electronic Research Announcements, 2007, 14: 1-6. doi: 10.3934/era.2007.14.1 |
[12] |
Richard Evan Schwartz. Outer billiards on the Penrose kite: Compactification and renormalization. Journal of Modern Dynamics, 2011, 5 (3) : 473-581. doi: 10.3934/jmd.2011.5.473 |
[13] |
Stefano Marò. Relativistic pendulum and invariant curves. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 1139-1162. doi: 10.3934/dcds.2015.35.1139 |
[14] |
Christopher Cox, Renato Feres. Differential geometry of rigid bodies collisions and non-standard billiards. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6065-6099. doi: 10.3934/dcds.2016065 |
[15] |
Entisar A.-L. Ali, G. Charlot. Local contact sub-Finslerian geometry for maximum norms in dimension 3. Mathematical Control and Related Fields, 2021, 11 (2) : 373-401. doi: 10.3934/mcrf.2020041 |
[16] |
Leonardo Mora. Homoclinic bifurcations, fat attractors and invariant curves. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 1133-1148. doi: 10.3934/dcds.2003.9.1133 |
[17] |
Jordi-Lluís Figueras, Àlex Haro. A note on the fractalization of saddle invariant curves in quasiperiodic systems. Discrete and Continuous Dynamical Systems - S, 2016, 9 (4) : 1095-1107. doi: 10.3934/dcdss.2016043 |
[18] |
Peng Huang, Xiong Li, Bin Liu. Invariant curves of smooth quasi-periodic mappings. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 131-154. doi: 10.3934/dcds.2018006 |
[19] |
Krzysztof Frączek, Ronggang Shi, Corinna Ulcigrai. Genericity on curves and applications: pseudo-integrable billiards, Eaton lenses and gap distributions. Journal of Modern Dynamics, 2018, 12: 55-122. doi: 10.3934/jmd.2018004 |
[20] |
Dennis I. Barrett, Rory Biggs, Claudiu C. Remsing, Olga Rossi. Invariant nonholonomic Riemannian structures on three-dimensional Lie groups. Journal of Geometric Mechanics, 2016, 8 (2) : 139-167. doi: 10.3934/jgm.2016001 |
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