-
Previous Article
Veech groups, irrational billiards and stable abelian differentials
- DCDS Home
- This Issue
-
Next Article
Multi-dimensional traveling fronts in bistable reaction-diffusion equations
Recurrence in generic staircases
1. | Aix-Marseille University, Centre de physique théorique, Fédération de Recherches des Unités de Mathématique de Marseille, and Institut de mathématiques de Luminy, Luminy, Case 907, F-13288 Marseille Cedex 9, France |
References:
[1] |
G. Cristadoro, M. Lenci and M. Seri, Recurrence for quenched random Lorentz tubes,, preprint, (). Google Scholar |
[2] |
E. Gutkin and S. Troubetzkoy, Directional flows and strong recurrence for polygonal billiards,, in, 362 (1996), 21.
|
[3] |
W. P. Hooper, Dynamics on an infinite surface with the lattice property,, \arXiv{0802.0189}., (). Google Scholar |
[4] |
W. P. Hooper and B. Weiss, Generalized staircases: Recurrence and symmetry,, preprint, (). Google Scholar |
[5] |
P. Hubert and B. Weiss, Dynamics on an infinite staircase,, preprint, (2008). Google Scholar |
[6] |
P. Hubert and G. Schmithüsen, Infinite translation surface with infinitely generated Veech groups,, 2009., (). Google Scholar |
[7] |
P. Hubert, S. Lelievre and S. Troubetzkoy, On the Ehrenfest wind-tree model: Periodic directions, recurrence, diffusion,, preprint, (). Google Scholar |
[8] |
S. Kerckhoff, H. Masur and J. Smillie, Ergodicity of billiard flows and quadratic differentials,, Annals of Math., 124 (1986), 293.
|
[9] |
, M. Lenci and S. Troubetzkoy,, in preparation., (). Google Scholar |
[10] |
Ǐ. Schmeling and S. Troubetzkoǐ, Inhomogeneous Diophantine approximation and angular recurrence for billiards in polygons,, Sb. Math. \textbf{194} (2003), 194 (2003), 295.
doi: 10.1070/SM2003v194n02ABEH000717. |
[11] |
K. Schmidt, "Cocyles on Ergodic Transformation Groups,", Macmillan Lectures in Mathematics, (1977). Google Scholar |
[12] |
S. Troubetzkoy, Recurrence and periodic billiard orbits in polygons,, Regul. Chaotic Dyn., 9 (2004), 1.
doi: 10.1070/RD2004v009n01ABEH000259. |
[13] |
S. Troubetzkoy, Typical recurrence for the Ehrenfest wind-tree model,, Journal of Statistical Physics, 141 (2010), 60.
doi: 10.1007/s10955-010-0026-5. |
[14] |
W. A. Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards,, Invent. Math., 97 (1989), 553.
doi: 10.1007/BF01388890. |
show all references
References:
[1] |
G. Cristadoro, M. Lenci and M. Seri, Recurrence for quenched random Lorentz tubes,, preprint, (). Google Scholar |
[2] |
E. Gutkin and S. Troubetzkoy, Directional flows and strong recurrence for polygonal billiards,, in, 362 (1996), 21.
|
[3] |
W. P. Hooper, Dynamics on an infinite surface with the lattice property,, \arXiv{0802.0189}., (). Google Scholar |
[4] |
W. P. Hooper and B. Weiss, Generalized staircases: Recurrence and symmetry,, preprint, (). Google Scholar |
[5] |
P. Hubert and B. Weiss, Dynamics on an infinite staircase,, preprint, (2008). Google Scholar |
[6] |
P. Hubert and G. Schmithüsen, Infinite translation surface with infinitely generated Veech groups,, 2009., (). Google Scholar |
[7] |
P. Hubert, S. Lelievre and S. Troubetzkoy, On the Ehrenfest wind-tree model: Periodic directions, recurrence, diffusion,, preprint, (). Google Scholar |
[8] |
S. Kerckhoff, H. Masur and J. Smillie, Ergodicity of billiard flows and quadratic differentials,, Annals of Math., 124 (1986), 293.
|
[9] |
, M. Lenci and S. Troubetzkoy,, in preparation., (). Google Scholar |
[10] |
Ǐ. Schmeling and S. Troubetzkoǐ, Inhomogeneous Diophantine approximation and angular recurrence for billiards in polygons,, Sb. Math. \textbf{194} (2003), 194 (2003), 295.
doi: 10.1070/SM2003v194n02ABEH000717. |
[11] |
K. Schmidt, "Cocyles on Ergodic Transformation Groups,", Macmillan Lectures in Mathematics, (1977). Google Scholar |
[12] |
S. Troubetzkoy, Recurrence and periodic billiard orbits in polygons,, Regul. Chaotic Dyn., 9 (2004), 1.
doi: 10.1070/RD2004v009n01ABEH000259. |
[13] |
S. Troubetzkoy, Typical recurrence for the Ehrenfest wind-tree model,, Journal of Statistical Physics, 141 (2010), 60.
doi: 10.1007/s10955-010-0026-5. |
[14] |
W. A. Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards,, Invent. Math., 97 (1989), 553.
doi: 10.1007/BF01388890. |
[1] |
Guido Cavallaro, Roberto Garra, Carlo Marchioro. Long time localization of modified surface quasi-geostrophic equations. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020336 |
[2] |
Hua Zhong, Xiaolin Fan, Shuyu Sun. The effect of surface pattern property on the advancing motion of three-dimensional droplets. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020366 |
[3] |
Tian Ma, Shouhong Wang. Topological phase transition III: Solar surface eruptions and sunspots. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 501-514. doi: 10.3934/dcdsb.2020350 |
[4] |
Karoline Disser. Global existence and uniqueness for a volume-surface reaction-nonlinear-diffusion system. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 321-330. doi: 10.3934/dcdss.2020326 |
[5] |
Björn Augner, Dieter Bothe. The fast-sorption and fast-surface-reaction limit of a heterogeneous catalysis model. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 533-574. doi: 10.3934/dcdss.2020406 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]