March  2007, 19(1): 89-102. doi: 10.3934/dcds.2007.19.89

Entropy of polyhedral billiard

1. 

Fédération de recherche des unités de mathématiques de Marseille, LATP, Faculté des sciences de Saint-Jérome, case cours A, Université Paul Cézanne, 13397 Marseille Cedex 20, France

Received  July 2006 Revised  February 2007 Published  June 2007

We consider the billiard map in a convex polyhedron of $\mathbb{R}^3$, and we prove that it is of zero topological entropy.
Citation: Nicolas Bedaride. Entropy of polyhedral billiard. Discrete and Continuous Dynamical Systems, 2007, 19 (1) : 89-102. doi: 10.3934/dcds.2007.19.89
[1]

John Kieffer and En-hui Yang. Ergodic behavior of graph entropy. Electronic Research Announcements, 1997, 3: 11-16.

[2]

Ryszard Rudnicki. An ergodic theory approach to chaos. Discrete and Continuous Dynamical Systems, 2015, 35 (2) : 757-770. doi: 10.3934/dcds.2015.35.757

[3]

Thierry de la Rue. An introduction to joinings in ergodic theory. Discrete and Continuous Dynamical Systems, 2006, 15 (1) : 121-142. doi: 10.3934/dcds.2006.15.121

[4]

Christian Wolf. A shift map with a discontinuous entropy function. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 319-329. doi: 10.3934/dcds.2020012

[5]

Wen Huang, Leiye Xu, Shengnan Xu. Ergodic measures of intermediate entropy for affine transformations of nilmanifolds. Electronic Research Archive, 2021, 29 (4) : 2819-2827. doi: 10.3934/era.2021015

[6]

Xiongping Dai, Yu Huang, Mingqing Xiao. Realization of joint spectral radius via Ergodic theory. Electronic Research Announcements, 2011, 18: 22-30. doi: 10.3934/era.2011.18.22

[7]

Cristina Lizana, Vilton Pinheiro, Paulo Varandas. Contribution to the ergodic theory of robustly transitive maps. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 353-365. doi: 10.3934/dcds.2015.35.353

[8]

Boris Kruglikov, Martin Rypdal. A piece-wise affine contracting map with positive entropy. Discrete and Continuous Dynamical Systems, 2006, 16 (2) : 393-394. doi: 10.3934/dcds.2006.16.393

[9]

David Burguet. Examples of $\mathcal{C}^r$ interval map with large symbolic extension entropy. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 873-899. doi: 10.3934/dcds.2010.26.873

[10]

El Houcein El Abdalaoui, Joanna Kułaga-Przymus, Mariusz Lemańczyk, Thierry de la Rue. The Chowla and the Sarnak conjectures from ergodic theory point of view. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 2899-2944. doi: 10.3934/dcds.2017125

[11]

Katayun Barmak, Eva Eggeling, Maria Emelianenko, Yekaterina Epshteyn, David Kinderlehrer, Richard Sharp, Shlomo Ta'asan. An entropy based theory of the grain boundary character distribution. Discrete and Continuous Dynamical Systems, 2011, 30 (2) : 427-454. doi: 10.3934/dcds.2011.30.427

[12]

Shuhei Hayashi. A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 2285-2313. doi: 10.3934/dcds.2020114

[13]

Jean-Paul Thouvenot. The work of Lewis Bowen on the entropy theory of non-amenable group actions. Journal of Modern Dynamics, 2019, 15: 133-141. doi: 10.3934/jmd.2019016

[14]

Steven M. Pederson. Non-turning Poincaré map and homoclinic tangencies in interval maps with non-constant topological entropy. Conference Publications, 2001, 2001 (Special) : 295-302. doi: 10.3934/proc.2001.2001.295

[15]

Earl Berkson. Fourier analysis methods in operator ergodic theory on super-reflexive Banach spaces. Electronic Research Announcements, 2010, 17: 90-103. doi: 10.3934/era.2010.17.90

[16]

Yves Derriennic. Some aspects of recent works on limit theorems in ergodic theory with special emphasis on the "central limit theorem''. Discrete and Continuous Dynamical Systems, 2006, 15 (1) : 143-158. doi: 10.3934/dcds.2006.15.143

[17]

Pavel Bachurin, Konstantin Khanin, Jens Marklof, Alexander Plakhov. Perfect retroreflectors and billiard dynamics. Journal of Modern Dynamics, 2011, 5 (1) : 33-48. doi: 10.3934/jmd.2011.5.33

[18]

Chantelle Blachut, Cecilia González-Tokman. A tale of two vortices: How numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems. Journal of Computational Dynamics, 2020, 7 (2) : 369-399. doi: 10.3934/jcd.2020015

[19]

David Cowan. A billiard model for a gas of particles with rotation. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 101-109. doi: 10.3934/dcds.2008.22.101

[20]

Mason A. Porter, Richard L. Liboff. The radially vibrating spherical quantum billiard. Conference Publications, 2001, 2001 (Special) : 310-318. doi: 10.3934/proc.2001.2001.310

2021 Impact Factor: 1.588

Metrics

  • PDF downloads (70)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]