-
Previous Article
Counting orbits of integral points in families of affine homogeneous varieties and diagonal flows
- JMD Home
- This Issue
-
Next Article
On the work of Sarig on countable Markov chains and thermodynamic formalism
On Omri Sarig's work on the dynamics on surfaces
1. | LPMA, Boîte Courrier 188, 4, Place Jussieu, 75252 PARIS cedex 05, France |
References:
[1] |
R. Adler and B. Weiss, Similarities of the Automorphisms of the Torus,, Memoirs of the Amer. Math. Soc., (1970).
|
[2] |
M. Babillot, On the classification of invariant measures for horosphere foliations on nilpotent covers of negatively curved manifolds,, in Random Walks and Geometry (ed. V. A. Kaimanovich), (2004), 319.
|
[3] |
K. Berg, Convolutions of invariant measures, maximal entropy,, Math. Systems Theory, 3 (1969), 146.
doi: 10.1007/BF01746521. |
[4] |
P. Berger, Properties of the maximal entropy measure and geometry of Hénon attractors,, , (2012). Google Scholar |
[5] |
M. Babillot and F. Ledrappier, Geodesic paths and horocycle flows on abelian covers,, in Lie Groups and Ergodic Theory (Mumbai, (1996), 1.
|
[6] |
R. Bowen, Periodic points and measures for Axiom $A$ diffeomorphisms,, Trans.Amer. Math. Soc., 154 (1971), 377.
|
[7] |
M. Boyle, D. Fiebig and U. Fiebig, Residual entropy, conditional entropy and subshift covers,, Forum Math., 14 (2002), 713.
doi: 10.1515/form.2002.031. |
[8] |
M. Burger, Horocycle flows on geometrically finite surfaces,, Duke Math. J., 61 (1990), 779.
doi: 10.1215/S0012-7094-90-06129-0. |
[9] |
D. Burguet, Symbolic extensions in intermediate smoothness on surfaces,, Ann. Sci. Éc. Norm. Sup. (4), 45 (2012), 337.
|
[10] |
J. Buzzi, Intrinsic ergodicity of smooth interval maps,, Israel J. Math., 100 (1997), 125.
doi: 10.1007/BF02773637. |
[11] |
S. G. Dani and J. Smillie, Uniform distribution of horocycle orbits for Fuchsian groups,, Duke Math. J., 51 (1984), 185.
doi: 10.1215/S0012-7094-84-05110-X. |
[12] |
T. Downarowicz and S. Newhouse, Symbolic extensions and smooth dynamical systems,, Invent. Math., 160 (2005), 453.
doi: 10.1007/s00222-004-0413-0. |
[13] |
N. Friedman and D. S. Ornstein, On isomorphism of weak Bernoulli transformations,, Advances Math., 5 (1970), 365.
doi: 10.1016/0001-8708(70)90010-1. |
[14] |
H. Furstenberg, The unique ergodicity of the horocycle flow,, Recent Advances in Topological Dynamics (Proc. Conf., (1972), 95.
|
[15] |
F. Hofbauer, On intrinsic ergodicity of piecewise monotonic transformations with positive entropy,, Israel J. Math., 34 (1979), 213.
doi: 10.1007/BF02761854. |
[16] |
A. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms,, Inst. Hautes Études Sci. Publ. Math., 51 (1980), 137.
|
[17] |
V. Kaloshin, Generic diffeomorphisms with superexponential growth of number of periodic orbits,, Comm. Math. Phys., 211 (2000), 253.
doi: 10.1007/s002200050811. |
[18] |
F. Ledrappier, Propriétés ergodiques des mesures de Sinaï,, Inst. Hautes Études Sci. Publ. Math., 59 (1984), 163.
|
[19] |
F. Ledrappier and O. Sarig, Invariant measures for horocycle flows on periodic hyperbolic surfaces,, Israel J. Math., 160 (2007), 281.
doi: 10.1007/s11856-007-0064-0. |
[20] |
S. Newhouse, Continuity properties of entropy,, Ann. Math. (2), 129 (1989), 215.
doi: 10.2307/1971492. |
[21] |
W. Parry, Intrinsic Markov chains,, Trans. Amer. Math. Soc., 112 (1964), 55.
doi: 10.1090/S0002-9947-1964-0161372-1. |
[22] |
S. J. Patterson, Spectral theory and Fuchsian groups,, Math. Proc. Cambridge Phil. Soc., 81 (1977), 59.
doi: 10.1017/S030500410000027X. |
[23] |
S. J. Patterson, Some examples of Fuchsian groups,, Proc. London Math. Soc. (3), 39 (1979), 276.
doi: 10.1112/plms/s3-39.2.276. |
[24] |
Y. B. Pesin, Characteristic Ljapunov exponents, and smooth ergodic theory,, Russian Math. Surveys, 32 (1977), 55.
doi: 10.1070/RM1977v032n04ABEH001639. |
[25] |
Y. Pesin, On the work of Omri Sarig on infinite Markov chains and thermodynamical formalism,, J. Modern Dynamics, (2014). Google Scholar |
[26] |
M. Ratner, On Raghunathan's measure conjecture,, Ann. Math. (2), 134 (1991), 545.
doi: 10.2307/2944357. |
[27] |
T. Roblin, Ergodicité et équidistribution en courbure négative,, Mém. Soc. Math. Fr. (N. S.), 95 (2003).
|
[28] |
O. Sarig, Invariant Radon measures for horocycle flows on Abelian covers,, Invent. Math., 157 (2004), 519.
doi: 10.1007/s00222-004-0357-4. |
[29] |
O. Sarig, The horocycle flow and the Laplacian on hyperbolic surfaces of infinite genus,, Geom. Funct. Anal., 19 (2010), 1757.
doi: 10.1007/s00039-010-0048-9. |
[30] |
O. Sarig, Bernoulli equilibrium states for surface diffeomorphisms,, J. Modern Dynamics, 5 (2011), 593.
doi: 10.3934/jmd.2011.5.593. |
[31] |
O. Sarig, Symbolic dynamics for surface diffeomorphisms with positive entropy,, J. Amer. Math. Soc., 26 (2013), 341.
doi: 10.1090/S0894-0347-2012-00758-9. |
[32] |
O. Sarig, Thermodynamic formalism for countable Markov shifts,, Ergodic Theory Dynam. Systems, 19 (1999), 1565.
doi: 10.1017/S0143385799146820. |
[33] |
B. Schapira, Equidistribution of the horocycles of a geomertically finite surface,, Int. Mat. Res. Not., (2005), 2447.
doi: 10.1155/IMRN.2005.2447. |
[34] |
M. Shub, Global Stability of Dynamical Systems,, Springer-Verlag, (1987).
doi: 10.1007/978-1-4757-1947-5. |
[35] |
Y. G. Sinaĭ, Construction of Markov partitions,, Functional Anal. Appl., 2 (1968), 245.
doi: 10.1007/BF01076126. |
[36] |
B. Weiss, Intrinsically ergodic systems,, Bull. Amer. Math. Soc., 76 (1970), 1266.
doi: 10.1090/S0002-9904-1970-12632-5. |
[37] |
L.-S. Young, Statistical properties of dynamical systems with some hyperbolicity,, Ann. Math. (2), 147 (1988), 585.
doi: 10.2307/120960. |
show all references
References:
[1] |
R. Adler and B. Weiss, Similarities of the Automorphisms of the Torus,, Memoirs of the Amer. Math. Soc., (1970).
|
[2] |
M. Babillot, On the classification of invariant measures for horosphere foliations on nilpotent covers of negatively curved manifolds,, in Random Walks and Geometry (ed. V. A. Kaimanovich), (2004), 319.
|
[3] |
K. Berg, Convolutions of invariant measures, maximal entropy,, Math. Systems Theory, 3 (1969), 146.
doi: 10.1007/BF01746521. |
[4] |
P. Berger, Properties of the maximal entropy measure and geometry of Hénon attractors,, , (2012). Google Scholar |
[5] |
M. Babillot and F. Ledrappier, Geodesic paths and horocycle flows on abelian covers,, in Lie Groups and Ergodic Theory (Mumbai, (1996), 1.
|
[6] |
R. Bowen, Periodic points and measures for Axiom $A$ diffeomorphisms,, Trans.Amer. Math. Soc., 154 (1971), 377.
|
[7] |
M. Boyle, D. Fiebig and U. Fiebig, Residual entropy, conditional entropy and subshift covers,, Forum Math., 14 (2002), 713.
doi: 10.1515/form.2002.031. |
[8] |
M. Burger, Horocycle flows on geometrically finite surfaces,, Duke Math. J., 61 (1990), 779.
doi: 10.1215/S0012-7094-90-06129-0. |
[9] |
D. Burguet, Symbolic extensions in intermediate smoothness on surfaces,, Ann. Sci. Éc. Norm. Sup. (4), 45 (2012), 337.
|
[10] |
J. Buzzi, Intrinsic ergodicity of smooth interval maps,, Israel J. Math., 100 (1997), 125.
doi: 10.1007/BF02773637. |
[11] |
S. G. Dani and J. Smillie, Uniform distribution of horocycle orbits for Fuchsian groups,, Duke Math. J., 51 (1984), 185.
doi: 10.1215/S0012-7094-84-05110-X. |
[12] |
T. Downarowicz and S. Newhouse, Symbolic extensions and smooth dynamical systems,, Invent. Math., 160 (2005), 453.
doi: 10.1007/s00222-004-0413-0. |
[13] |
N. Friedman and D. S. Ornstein, On isomorphism of weak Bernoulli transformations,, Advances Math., 5 (1970), 365.
doi: 10.1016/0001-8708(70)90010-1. |
[14] |
H. Furstenberg, The unique ergodicity of the horocycle flow,, Recent Advances in Topological Dynamics (Proc. Conf., (1972), 95.
|
[15] |
F. Hofbauer, On intrinsic ergodicity of piecewise monotonic transformations with positive entropy,, Israel J. Math., 34 (1979), 213.
doi: 10.1007/BF02761854. |
[16] |
A. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms,, Inst. Hautes Études Sci. Publ. Math., 51 (1980), 137.
|
[17] |
V. Kaloshin, Generic diffeomorphisms with superexponential growth of number of periodic orbits,, Comm. Math. Phys., 211 (2000), 253.
doi: 10.1007/s002200050811. |
[18] |
F. Ledrappier, Propriétés ergodiques des mesures de Sinaï,, Inst. Hautes Études Sci. Publ. Math., 59 (1984), 163.
|
[19] |
F. Ledrappier and O. Sarig, Invariant measures for horocycle flows on periodic hyperbolic surfaces,, Israel J. Math., 160 (2007), 281.
doi: 10.1007/s11856-007-0064-0. |
[20] |
S. Newhouse, Continuity properties of entropy,, Ann. Math. (2), 129 (1989), 215.
doi: 10.2307/1971492. |
[21] |
W. Parry, Intrinsic Markov chains,, Trans. Amer. Math. Soc., 112 (1964), 55.
doi: 10.1090/S0002-9947-1964-0161372-1. |
[22] |
S. J. Patterson, Spectral theory and Fuchsian groups,, Math. Proc. Cambridge Phil. Soc., 81 (1977), 59.
doi: 10.1017/S030500410000027X. |
[23] |
S. J. Patterson, Some examples of Fuchsian groups,, Proc. London Math. Soc. (3), 39 (1979), 276.
doi: 10.1112/plms/s3-39.2.276. |
[24] |
Y. B. Pesin, Characteristic Ljapunov exponents, and smooth ergodic theory,, Russian Math. Surveys, 32 (1977), 55.
doi: 10.1070/RM1977v032n04ABEH001639. |
[25] |
Y. Pesin, On the work of Omri Sarig on infinite Markov chains and thermodynamical formalism,, J. Modern Dynamics, (2014). Google Scholar |
[26] |
M. Ratner, On Raghunathan's measure conjecture,, Ann. Math. (2), 134 (1991), 545.
doi: 10.2307/2944357. |
[27] |
T. Roblin, Ergodicité et équidistribution en courbure négative,, Mém. Soc. Math. Fr. (N. S.), 95 (2003).
|
[28] |
O. Sarig, Invariant Radon measures for horocycle flows on Abelian covers,, Invent. Math., 157 (2004), 519.
doi: 10.1007/s00222-004-0357-4. |
[29] |
O. Sarig, The horocycle flow and the Laplacian on hyperbolic surfaces of infinite genus,, Geom. Funct. Anal., 19 (2010), 1757.
doi: 10.1007/s00039-010-0048-9. |
[30] |
O. Sarig, Bernoulli equilibrium states for surface diffeomorphisms,, J. Modern Dynamics, 5 (2011), 593.
doi: 10.3934/jmd.2011.5.593. |
[31] |
O. Sarig, Symbolic dynamics for surface diffeomorphisms with positive entropy,, J. Amer. Math. Soc., 26 (2013), 341.
doi: 10.1090/S0894-0347-2012-00758-9. |
[32] |
O. Sarig, Thermodynamic formalism for countable Markov shifts,, Ergodic Theory Dynam. Systems, 19 (1999), 1565.
doi: 10.1017/S0143385799146820. |
[33] |
B. Schapira, Equidistribution of the horocycles of a geomertically finite surface,, Int. Mat. Res. Not., (2005), 2447.
doi: 10.1155/IMRN.2005.2447. |
[34] |
M. Shub, Global Stability of Dynamical Systems,, Springer-Verlag, (1987).
doi: 10.1007/978-1-4757-1947-5. |
[35] |
Y. G. Sinaĭ, Construction of Markov partitions,, Functional Anal. Appl., 2 (1968), 245.
doi: 10.1007/BF01076126. |
[36] |
B. Weiss, Intrinsically ergodic systems,, Bull. Amer. Math. Soc., 76 (1970), 1266.
doi: 10.1090/S0002-9904-1970-12632-5. |
[37] |
L.-S. Young, Statistical properties of dynamical systems with some hyperbolicity,, Ann. Math. (2), 147 (1988), 585.
doi: 10.2307/120960. |
[1] |
The Editors. The 2018 Michael Brin Prize in Dynamical Systems. Journal of Modern Dynamics, 2019, 15: 425-426. doi: 10.3934/jmd.2019025 |
[2] |
The Editors. The 2015 Michael Brin Prize in Dynamical Systems. Journal of Modern Dynamics, 2016, 10: 173-174. doi: 10.3934/jmd.2016.10.173 |
[3] |
The Editors. The 2019 Michael Brin Prize in Dynamical Systems. Journal of Modern Dynamics, 2020, 16: 349-350. doi: 10.3934/jmd.2020013 |
[4] |
The Editors. The 2017 Michael Brin Prize in Dynamical Systems. Journal of Modern Dynamics, 2019, 15: 131-132. doi: 10.3934/jmd.2019015 |
[5] |
The Editors. The 2013 Michael Brin Prize in Dynamical Systems. Journal of Modern Dynamics, 2014, 8 (1) : i-ii. doi: 10.3934/jmd.2014.8.1i |
[6] |
The Editors. The 2008 Michael Brin Prize in Dynamical Systems. Journal of Modern Dynamics, 2008, 2 (3) : i-ii. doi: 10.3934/jmd.2008.2.3i |
[7] |
The Editors. The 2009 Michael Brin Prize in Dynamical Systems. Journal of Modern Dynamics, 2010, 4 (2) : i-ii. doi: 10.3934/jmd.2010.4.2i |
[8] |
The Editors. The 2011 Michael Brin Prize in Dynamical Systems. Journal of Modern Dynamics, 2012, 6 (2) : i-ii. doi: 10.3934/jmd.2012.6.2i |
[9] |
Yakov Pesin. On the work of Sarig on countable Markov chains and thermodynamic formalism. Journal of Modern Dynamics, 2014, 8 (1) : 1-14. doi: 10.3934/jmd.2014.8.1 |
[10] |
Mikhail Lyubich. Forty years of unimodal dynamics: On the occasion of Artur Avila winning the Brin Prize. Journal of Modern Dynamics, 2012, 6 (2) : 183-203. doi: 10.3934/jmd.2012.6.183 |
[11] |
Enrique R. Pujals, Federico Rodriguez Hertz. Critical points for surface diffeomorphisms. Journal of Modern Dynamics, 2007, 1 (4) : 615-648. doi: 10.3934/jmd.2007.1.615 |
[12] |
Manfred G. Madritsch. Non-normal numbers with respect to Markov partitions. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 663-676. doi: 10.3934/dcds.2014.34.663 |
[13] |
Michael Jakobson, Lucia D. Simonelli. Countable Markov partitions suitable for thermodynamic formalism. Journal of Modern Dynamics, 2018, 13: 199-219. doi: 10.3934/jmd.2018018 |
[14] |
Omri M. Sarig. Bernoulli equilibrium states for surface diffeomorphisms. Journal of Modern Dynamics, 2011, 5 (3) : 593-608. doi: 10.3934/jmd.2011.5.593 |
[15] |
Giovanni Forni. On the Brin Prize work of Artur Avila in Teichmüller dynamics and interval-exchange transformations. Journal of Modern Dynamics, 2012, 6 (2) : 139-182. doi: 10.3934/jmd.2012.6.139 |
[16] |
Francois Ledrappier and Omri Sarig. Invariant measures for the horocycle flow on periodic hyperbolic surfaces. Electronic Research Announcements, 2005, 11: 89-94. |
[17] |
Thomas Ward, Yuki Yayama. Markov partitions reflecting the geometry of $\times2$, $\times3$. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 613-624. doi: 10.3934/dcds.2009.24.613 |
[18] |
Alfonso Artigue. Robustly N-expansive surface diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 2016, 36 (5) : 2367-2376. doi: 10.3934/dcds.2016.36.2367 |
[19] |
C. Morales. On spiral periodic points and saddles for surface diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 1191-1195. doi: 10.3934/dcds.2011.29.1191 |
[20] |
Fernando Alcalde Cuesta, Françoise Dal'Bo, Matilde Martínez, Alberto Verjovsky. Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4619-4635. doi: 10.3934/dcds.2016001 |
2019 Impact Factor: 0.465
Tools
Metrics
Other articles
by authors
[Back to Top]