-
Previous Article
Boundary unitary representations-irreducibility and rigidity
- JMD Home
- This Issue
-
Next Article
Shimura and Teichmüller curves
Perfect retroreflectors and billiard dynamics
1. | Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651, United States |
2. | Department of Mathematics, University of Toronto, 40 St. George St., Toronto, Ontario M5S 2E4, Canada |
3. | School of Mathematics, University of Bristol, Bristol BS8 1TW |
4. | Department of Mathematics, University of Aveiro, Aveiro 3810-193, Portugal |
References:
[1] |
M. Boshernitzan, A condition for minimal interval-exchange maps to be uniquely ergodic, Duke Math. J., 52 (1985), 723-752.
doi: 10.1215/S0012-7094-85-05238-X. |
[2] |
M. Boshernitzan, A condition for unique ergodicity of minimal symbolic flows, Ergodic Theory Dynam. Systems, 12 (1992), 425-428.
doi: 10.1017/S0143385700006866. |
[3] |
M. Boshernitzan and A. Nogueira, Generalized functions of interval-exchange maps, Ergodic Theory Dynam. Systems, 24 (2004), 697-705.
doi: 10.1017/S0143385704000021. |
[4] |
J. E. Eaton, On spherically symmetric lenses, Trans. IRE Antennas Propag., 4 (1952) 66-71. |
[5] |
P. Hubert, S. Lelièvre and S. Troubetzkoy, The Ehrenfest wind-tree model: Periodic directions, recurrence, diffusion,, \arXiv{0912.2891}., ().
|
[6] |
A. Katok and A. Stepin, Approximations in ergodic theory, (Russian) Uspehi Mat. Nauk, 22 (1967), 81-106. |
[7] |
M. Loeve, "Probability Theory I," Fourth edition, Graduate Texts in Mathematics, Vol. 45, Springer-Verlag, New York-Heidelberg, 1977. |
[8] |
J. Marklof, Distribution modulo one and Ratner's theorem, Equidistribution in Number Theory, An Introduction, 217-244, NATO Sci. Ser. II Math. Phys. Chem., 237, Springer, Dordrecht, 2007. |
[9] |
J. Marklof, The $n$-point correlations between values of a linear form, With an appendix by Zeév Rudnick, Ergodic Theory Dynam. Systems, 20 (2000), 1127-1172.
doi: 10.1017/S0143385700000626. |
[10] |
J. Marklof and A. Strömbergsson, The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems, Annals of Math., 172 (2010), 1949-2033.
doi: 10.4007/annals.2010.172.1949. |
[11] |
A. E. Mazel and Y. G. Sinai, A limiting distribution connected with fractional parts of linear forms, Ideas and methods in mathematical analysis, stochastics, and applications (Oslo, 1988), 220-229, Cambridge Univ. Press, Cambridge, 1992. |
[12] |
A. Plakhov and P. Gouveia, Problems of maximal mean resistance on the plane, Nonlinearity, 20 (2007), 2271-2287.
doi: 10.1088/0951-7715/20/9/013. |
[13] |
C. L. Siegel, "Lectures on the Geometry of Numbers," Notes by B. Friedman, Rewritten by Komaravolu Chandrasekharan with the assistance of Rudolf Suter, With a preface by Chandrasekharan. Springer-Verlag, Berlin, 1989. |
[14] |
T. Tyc, U. Leonhardt, Transmutation of singularities in optical instruments, New J. Physics, 10 (2008), 115038 (8pp). |
[15] |
W. A. Veech, Boshernitzan's criterion for unique ergodicity of an interval-exchange transformation, Ergodic Theory Dynam. Systems, 7 (1987), 149-153.
doi: 10.1017/S0143385700003862. |
show all references
References:
[1] |
M. Boshernitzan, A condition for minimal interval-exchange maps to be uniquely ergodic, Duke Math. J., 52 (1985), 723-752.
doi: 10.1215/S0012-7094-85-05238-X. |
[2] |
M. Boshernitzan, A condition for unique ergodicity of minimal symbolic flows, Ergodic Theory Dynam. Systems, 12 (1992), 425-428.
doi: 10.1017/S0143385700006866. |
[3] |
M. Boshernitzan and A. Nogueira, Generalized functions of interval-exchange maps, Ergodic Theory Dynam. Systems, 24 (2004), 697-705.
doi: 10.1017/S0143385704000021. |
[4] |
J. E. Eaton, On spherically symmetric lenses, Trans. IRE Antennas Propag., 4 (1952) 66-71. |
[5] |
P. Hubert, S. Lelièvre and S. Troubetzkoy, The Ehrenfest wind-tree model: Periodic directions, recurrence, diffusion,, \arXiv{0912.2891}., ().
|
[6] |
A. Katok and A. Stepin, Approximations in ergodic theory, (Russian) Uspehi Mat. Nauk, 22 (1967), 81-106. |
[7] |
M. Loeve, "Probability Theory I," Fourth edition, Graduate Texts in Mathematics, Vol. 45, Springer-Verlag, New York-Heidelberg, 1977. |
[8] |
J. Marklof, Distribution modulo one and Ratner's theorem, Equidistribution in Number Theory, An Introduction, 217-244, NATO Sci. Ser. II Math. Phys. Chem., 237, Springer, Dordrecht, 2007. |
[9] |
J. Marklof, The $n$-point correlations between values of a linear form, With an appendix by Zeév Rudnick, Ergodic Theory Dynam. Systems, 20 (2000), 1127-1172.
doi: 10.1017/S0143385700000626. |
[10] |
J. Marklof and A. Strömbergsson, The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems, Annals of Math., 172 (2010), 1949-2033.
doi: 10.4007/annals.2010.172.1949. |
[11] |
A. E. Mazel and Y. G. Sinai, A limiting distribution connected with fractional parts of linear forms, Ideas and methods in mathematical analysis, stochastics, and applications (Oslo, 1988), 220-229, Cambridge Univ. Press, Cambridge, 1992. |
[12] |
A. Plakhov and P. Gouveia, Problems of maximal mean resistance on the plane, Nonlinearity, 20 (2007), 2271-2287.
doi: 10.1088/0951-7715/20/9/013. |
[13] |
C. L. Siegel, "Lectures on the Geometry of Numbers," Notes by B. Friedman, Rewritten by Komaravolu Chandrasekharan with the assistance of Rudolf Suter, With a preface by Chandrasekharan. Springer-Verlag, Berlin, 1989. |
[14] |
T. Tyc, U. Leonhardt, Transmutation of singularities in optical instruments, New J. Physics, 10 (2008), 115038 (8pp). |
[15] |
W. A. Veech, Boshernitzan's criterion for unique ergodicity of an interval-exchange transformation, Ergodic Theory Dynam. Systems, 7 (1987), 149-153.
doi: 10.1017/S0143385700003862. |
[1] |
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 |
[2] |
Philippe Marie, Jérôme Rousseau. Recurrence for random dynamical systems. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 1-16. doi: 10.3934/dcds.2011.30.1 |
[3] |
Abdelhamid Adouani, Habib Marzougui. Computation of rotation numbers for a class of PL-circle homeomorphisms. Discrete and Continuous Dynamical Systems, 2012, 32 (10) : 3399-3419. doi: 10.3934/dcds.2012.32.3399 |
[4] |
Vincent Penné, Benoît Saussol, Sandro Vaienti. Dimensions for recurrence times: topological and dynamical properties. Discrete and Continuous Dynamical Systems, 1999, 5 (4) : 783-798. doi: 10.3934/dcds.1999.5.783 |
[5] |
Piotr Oprocha. Chain recurrence in multidimensional time discrete dynamical systems. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 1039-1056. doi: 10.3934/dcds.2008.20.1039 |
[6] |
Benoît Saussol. Recurrence rate in rapidly mixing dynamical systems. Discrete and Continuous Dynamical Systems, 2006, 15 (1) : 259-267. doi: 10.3934/dcds.2006.15.259 |
[7] |
Alexander Plakhov. Mathematical retroreflectors. Discrete and Continuous Dynamical Systems, 2011, 30 (4) : 1211-1235. doi: 10.3934/dcds.2011.30.1211 |
[8] |
Nasab Yassine. Quantitative recurrence of some dynamical systems preserving an infinite measure in dimension one. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 343-361. doi: 10.3934/dcds.2018017 |
[9] |
Oliver Díaz-Espinosa, Rafael de la Llave. Renormalization and central limit theorem for critical dynamical systems with weak external noise. Journal of Modern Dynamics, 2007, 1 (3) : 477-543. doi: 10.3934/jmd.2007.1.477 |
[10] |
Malo Jézéquel. Parameter regularity of dynamical determinants of expanding maps of the circle and an application to linear response. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 927-958. doi: 10.3934/dcds.2019039 |
[11] |
Antonio Algaba, Estanislao Gamero, Cristóbal García. The reversibility problem for quasi-homogeneous dynamical systems. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3225-3236. doi: 10.3934/dcds.2013.33.3225 |
[12] |
Laura Cremaschi, Carlo Mantegazza. Short-time existence of the second order renormalization group flow in dimension three. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 5787-5798. doi: 10.3934/dcds.2015.35.5787 |
[13] |
T. Tachim Medjo. Averaging of an homogeneous two-phase flow model with oscillating external forces. Discrete and Continuous Dynamical Systems, 2012, 32 (10) : 3665-3690. doi: 10.3934/dcds.2012.32.3665 |
[14] |
Paul Deuring, Stanislav Kračmar, Šárka Nečasová. A leading term for the velocity of stationary viscous incompressible flow around a rigid body performing a rotation and a translation. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 1389-1409. doi: 10.3934/dcds.2017057 |
[15] |
Matthieu Hillairet, Ayman Moussa, Franck Sueur. On the effect of polydispersity and rotation on the Brinkman force induced by a cloud of particles on a viscous incompressible flow. Kinetic and Related Models, 2019, 12 (4) : 681-701. doi: 10.3934/krm.2019026 |
[16] |
A. A. Pinto, D. Sullivan. The circle and the solenoid. Discrete and Continuous Dynamical Systems, 2006, 16 (2) : 463-504. doi: 10.3934/dcds.2006.16.463 |
[17] |
María Anguiano, Francisco Javier Suárez-Grau. Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions. Networks and Heterogeneous Media, 2019, 14 (2) : 289-316. doi: 10.3934/nhm.2019012 |
[18] |
De Tang. Dynamical behavior for a Lotka-Volterra weak competition system in advective homogeneous environment. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 4913-4928. doi: 10.3934/dcdsb.2019037 |
[19] |
Chihurn Kim, Dong Han Kim. On the law of logarithm of the recurrence time. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 581-587. doi: 10.3934/dcds.2004.10.581 |
[20] |
Petr Kůrka, Vincent Penné, Sandro Vaienti. Dynamically defined recurrence dimension. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 137-146. doi: 10.3934/dcds.2002.8.137 |
2020 Impact Factor: 0.848
Tools
Metrics
Other articles
by authors
[Back to Top]