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Bernoulli equilibrium states for surface diffeomorphisms
1. | Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, POB 26, Rehovot, Israel |
References:
[1] |
R. L. Adler and B. Weiss, "Similarity of Automorphisms of the Torus,", Memoirs of the American Mathematical Society, (1970).
|
[2] |
R. L. Adler, P. Shields and M. Smorodinsky, Irreducible Markov shifts,, The Annals of Math. Statistics, 43 (1972), 1027.
doi: 10.1214/aoms/1177692569. |
[3] |
L. Barreira and Y. Pesin, "Nonuniform Hyperbolicity. Dynamics of Systems with Nonzero Lyapunov Exponents,", Encyclopedia of Mathematics and its Applications, 115 (2007).
|
[4] |
R. Bowen, Bernoulli equilibrium states for Axiom A diffeomorphisms,, Math. Systems Theory, 8 (): 289.
doi: 10.1007/BF01780576. |
[5] |
R. Bowen, "Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms,", Lecture Notes in Mathematics, 470 (1975).
|
[6] |
J. Buzzi, Maximal entropy measures for piecewise affine surface homeomorphisms,, Ergodic Theory Dynam. Systems, 29 (2009), 1723.
doi: 10.1017/S0143385708000953. |
[7] |
J. Buzzi and O. Sarig, Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps,, Ergodic Th. & Dynam. Syst., 23 (2003), 1383.
|
[8] |
B. M. Gurevič, Shift entropy and Markov measures in the space of paths of a countable graph,, (Russian), 192 (1970), 963.
|
[9] |
B. P. Kitchens, "Symbolic Dynamics. One-Sided, Two-Sided and Countable State Markov Shifts,", Universitext, (1998).
|
[10] |
F. Ledrappier, Propriétés ergodiques de mesures de Sinaï,, Inst. Hautes Études Sci. Publ. Math. No., 59 (1984), 163.
|
[11] |
F. Ledrappier and L.-S. Young, The metric entropy of diffeomorphisms. I. Characterization of measures satisfying Pesin's entropy formula,, Ann. of Math. (2), 122 (1985), 509.
doi: 10.2307/1971328. |
[12] |
S. Newhouse, Continuity properties of entropy,, Annals of Math. (2), 129 (1989), 215.
doi: 10.2307/1971492. |
[13] |
D. Ornstein, Factors of Bernoulli shifts are Bernoulli shifts,, Adv. in Math., 5 (1970), 349.
doi: 10.1016/0001-8708(70)90009-5. |
[14] |
D. Ornstein, Two Bernoulli shifts with infinite entropy are isomorphic,, Adv. in Math., 5 (1970), 339.
doi: 10.1016/0001-8708(70)90008-3. |
[15] |
D. Ornstein, Imbedding Bernoulli shifts in flows,, in, (1970), 178.
|
[16] |
D. Ornstein and N. A. Friedman, On isomorphism of weak Bernoulli transformations,, Adv. in Math., 5 (1970), 365.
doi: 10.1016/0001-8708(70)90010-1. |
[17] |
D. Ornstein and B. Weiss, On the Bernoulli nature of systems with some hyperbolic structure,, Ergodic Theory Dynam. Systems, 18 (1998), 441.
doi: 10.1017/S0143385798100354. |
[18] |
W. Parry, Intrinsic Markov chains,, Trans. Amer. Math. Soc., 112 (1964), 55.
doi: 10.1090/S0002-9947-1964-0161372-1. |
[19] |
Y. Pesin, Characteristic Ljapunov exponents and smooth ergodic theory,, Uspehi, 32 (1977), 55.
|
[20] |
M. Ratner, Anosov flows with Gibbs measures are also Bernoullian,, Israel J. Math., 17 (1974), 380.
doi: 10.1007/BF02757140. |
[21] |
R. Ruelle, A measure associated with axiom-A attractors,, Amer. J. Math., 98 (1976), 619.
doi: 10.2307/2373810. |
[22] |
O. M. Sarig, Thermodynamic formalism for null recurrent potentials,, Israel J. Math., 121 (2001), 285.
doi: 10.1007/BF02802508. |
[23] |
O. M. Sarig, Symbolic dynamics for surface diffeomorphisms with positive entropy,, submitted., (). Google Scholar |
[24] |
P. Walters, Ruelle's operator theorem and g-measures,, Trans. Amer. Math. Soc., 214 (1975), 375.
|
[25] |
P. Walters, "Ergodic Theory, Introductory Lectures,", Lecture Notes in Mathematics, 458 (1975).
|
[26] |
P. Walters, Regularity conditions and Bernoulli properties of equilibrium states and g-measures,, J. London Math. Soc. (2), 71 (2005), 379.
doi: 10.1112/S0024610704006076. |
show all references
References:
[1] |
R. L. Adler and B. Weiss, "Similarity of Automorphisms of the Torus,", Memoirs of the American Mathematical Society, (1970).
|
[2] |
R. L. Adler, P. Shields and M. Smorodinsky, Irreducible Markov shifts,, The Annals of Math. Statistics, 43 (1972), 1027.
doi: 10.1214/aoms/1177692569. |
[3] |
L. Barreira and Y. Pesin, "Nonuniform Hyperbolicity. Dynamics of Systems with Nonzero Lyapunov Exponents,", Encyclopedia of Mathematics and its Applications, 115 (2007).
|
[4] |
R. Bowen, Bernoulli equilibrium states for Axiom A diffeomorphisms,, Math. Systems Theory, 8 (): 289.
doi: 10.1007/BF01780576. |
[5] |
R. Bowen, "Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms,", Lecture Notes in Mathematics, 470 (1975).
|
[6] |
J. Buzzi, Maximal entropy measures for piecewise affine surface homeomorphisms,, Ergodic Theory Dynam. Systems, 29 (2009), 1723.
doi: 10.1017/S0143385708000953. |
[7] |
J. Buzzi and O. Sarig, Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps,, Ergodic Th. & Dynam. Syst., 23 (2003), 1383.
|
[8] |
B. M. Gurevič, Shift entropy and Markov measures in the space of paths of a countable graph,, (Russian), 192 (1970), 963.
|
[9] |
B. P. Kitchens, "Symbolic Dynamics. One-Sided, Two-Sided and Countable State Markov Shifts,", Universitext, (1998).
|
[10] |
F. Ledrappier, Propriétés ergodiques de mesures de Sinaï,, Inst. Hautes Études Sci. Publ. Math. No., 59 (1984), 163.
|
[11] |
F. Ledrappier and L.-S. Young, The metric entropy of diffeomorphisms. I. Characterization of measures satisfying Pesin's entropy formula,, Ann. of Math. (2), 122 (1985), 509.
doi: 10.2307/1971328. |
[12] |
S. Newhouse, Continuity properties of entropy,, Annals of Math. (2), 129 (1989), 215.
doi: 10.2307/1971492. |
[13] |
D. Ornstein, Factors of Bernoulli shifts are Bernoulli shifts,, Adv. in Math., 5 (1970), 349.
doi: 10.1016/0001-8708(70)90009-5. |
[14] |
D. Ornstein, Two Bernoulli shifts with infinite entropy are isomorphic,, Adv. in Math., 5 (1970), 339.
doi: 10.1016/0001-8708(70)90008-3. |
[15] |
D. Ornstein, Imbedding Bernoulli shifts in flows,, in, (1970), 178.
|
[16] |
D. Ornstein and N. A. Friedman, On isomorphism of weak Bernoulli transformations,, Adv. in Math., 5 (1970), 365.
doi: 10.1016/0001-8708(70)90010-1. |
[17] |
D. Ornstein and B. Weiss, On the Bernoulli nature of systems with some hyperbolic structure,, Ergodic Theory Dynam. Systems, 18 (1998), 441.
doi: 10.1017/S0143385798100354. |
[18] |
W. Parry, Intrinsic Markov chains,, Trans. Amer. Math. Soc., 112 (1964), 55.
doi: 10.1090/S0002-9947-1964-0161372-1. |
[19] |
Y. Pesin, Characteristic Ljapunov exponents and smooth ergodic theory,, Uspehi, 32 (1977), 55.
|
[20] |
M. Ratner, Anosov flows with Gibbs measures are also Bernoullian,, Israel J. Math., 17 (1974), 380.
doi: 10.1007/BF02757140. |
[21] |
R. Ruelle, A measure associated with axiom-A attractors,, Amer. J. Math., 98 (1976), 619.
doi: 10.2307/2373810. |
[22] |
O. M. Sarig, Thermodynamic formalism for null recurrent potentials,, Israel J. Math., 121 (2001), 285.
doi: 10.1007/BF02802508. |
[23] |
O. M. Sarig, Symbolic dynamics for surface diffeomorphisms with positive entropy,, submitted., (). Google Scholar |
[24] |
P. Walters, Ruelle's operator theorem and g-measures,, Trans. Amer. Math. Soc., 214 (1975), 375.
|
[25] |
P. Walters, "Ergodic Theory, Introductory Lectures,", Lecture Notes in Mathematics, 458 (1975).
|
[26] |
P. Walters, Regularity conditions and Bernoulli properties of equilibrium states and g-measures,, J. London Math. Soc. (2), 71 (2005), 379.
doi: 10.1112/S0024610704006076. |
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