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Statistical properties of diffeomorphisms with weak invariant manifolds
1. | Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal, Portugal |
References:
[1] |
J. F. Alves and V. Pinheiro, Slow rates of mixing for dynamical systems with hyperbolic structures, J. Stat. Phys., 131 (2008), 505-534.
doi: 10.1007/s10955-008-9482-6. |
[2] |
J. F. Alves and V. Pinheiro, Gibbs-Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction, Adv. Math., 223 (2010), 1706-1730.
doi: 10.1016/j.aim.2009.10.010. |
[3] |
V. Araújo, Large deviations for semiflows over a non-uniformly expanding base, Bull. Braz. Math. Soc. (N.S.), 38 (2007), 335-376.
doi: 10.1007/s00574-007-0049-y. |
[4] |
V. Araújo and M. J. Pacifico, Large deviations for non-uniformly expanding maps, J. Stat. Phys., 125 (2006), 415-457.
doi: 10.1007/s10955-006-9183-y. |
[5] |
R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, vol. 470, Springer, New York, 1975. |
[6] |
M. Benedicks and L.-S. Young, Markov extensions and decay of correlations for certain Hénon maps, Astérisque, 261 (2000), 13-56. |
[7] |
Y. Kifer, Large deviations in dynamical systems and stochastic processes, Trans. Amer. Math. Soc., 321 (1990), 505-524.
doi: 10.1090/S0002-9947-1990-1025756-7. |
[8] |
A. Lopes, Entropy and large deviations, Nonlinearity, 3 (1990), 527-546.
doi: 10.1088/0951-7715/3/2/013. |
[9] |
R. Mañé, Ergodic Theory and Differentiable Dynamics, Springer-Verlag, Berlin, 1987.
doi: 10.1007/978-3-642-70335-5. |
[10] |
I. Melbourne, Large and moderate deviations for slowly mixing dynamical systems, Proc. Amer. Math. Soc., 137 (2009), 1735-1741.
doi: 10.1090/S0002-9939-08-09751-7. |
[11] |
I. Melbourne and M. Nicol, Almost sure invariance principle for nonuniformly hyperbolic systems, Commun. Math. Phys., 260 (2005), 131-146.
doi: 10.1007/s00220-005-1407-5. |
[12] |
I. Melbourne and M. Nicol, Large deviations for nonuniformly hyperbolic systems, Trans. Amer. Math. Soc., 360 (2000), 6661-6676.
doi: 10.1090/S0002-9947-08-04520-0. |
[13] |
S. Orei and S. Pelikan, Large deviations principles for stationary processes, Ann. Probab., 16 (1988), 1481-1495.
doi: 10.1214/aop/1176991579. |
[14] |
D. Ruelle, A measure associated with Axiom A attractors, Am. J. Math., 98 (1976), 619-654.
doi: 10.2307/2373810. |
[15] |
E. Rio, Théorie Asymptotique des Processus Aléatoires Faiblement Dépendants, Mathématiques & Applications(Berlin) [Mathematics and Applications] 31, Springer-Verlag, Berlin, 2000. |
[16] |
Ya. Sinai, Gibbs measure in ergodic theory, Russ. Math. Surv., 27 (1972), 21-64. |
[17] |
S. Waddington, Large deviations asymptotics for Anosov flows, Ann. Inst. H. Poincaré Anal. Non Linéaire, 13 (1996), 445-484. |
[18] |
L.-S. Young, Large deviations in dynamical systems, Trans. Amer. Math. Soc., 318 (1990), 525-543.
doi: 10.2307/2001318. |
[19] |
L.-S. Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. Math., 147 (1998), 585-650.
doi: 10.2307/120960. |
[20] |
L.-S. Young, Recurrence times and rates of mixing, Israel J. Math., 110 (1999), 153-188.
doi: 10.1007/BF02808180. |
show all references
References:
[1] |
J. F. Alves and V. Pinheiro, Slow rates of mixing for dynamical systems with hyperbolic structures, J. Stat. Phys., 131 (2008), 505-534.
doi: 10.1007/s10955-008-9482-6. |
[2] |
J. F. Alves and V. Pinheiro, Gibbs-Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction, Adv. Math., 223 (2010), 1706-1730.
doi: 10.1016/j.aim.2009.10.010. |
[3] |
V. Araújo, Large deviations for semiflows over a non-uniformly expanding base, Bull. Braz. Math. Soc. (N.S.), 38 (2007), 335-376.
doi: 10.1007/s00574-007-0049-y. |
[4] |
V. Araújo and M. J. Pacifico, Large deviations for non-uniformly expanding maps, J. Stat. Phys., 125 (2006), 415-457.
doi: 10.1007/s10955-006-9183-y. |
[5] |
R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, vol. 470, Springer, New York, 1975. |
[6] |
M. Benedicks and L.-S. Young, Markov extensions and decay of correlations for certain Hénon maps, Astérisque, 261 (2000), 13-56. |
[7] |
Y. Kifer, Large deviations in dynamical systems and stochastic processes, Trans. Amer. Math. Soc., 321 (1990), 505-524.
doi: 10.1090/S0002-9947-1990-1025756-7. |
[8] |
A. Lopes, Entropy and large deviations, Nonlinearity, 3 (1990), 527-546.
doi: 10.1088/0951-7715/3/2/013. |
[9] |
R. Mañé, Ergodic Theory and Differentiable Dynamics, Springer-Verlag, Berlin, 1987.
doi: 10.1007/978-3-642-70335-5. |
[10] |
I. Melbourne, Large and moderate deviations for slowly mixing dynamical systems, Proc. Amer. Math. Soc., 137 (2009), 1735-1741.
doi: 10.1090/S0002-9939-08-09751-7. |
[11] |
I. Melbourne and M. Nicol, Almost sure invariance principle for nonuniformly hyperbolic systems, Commun. Math. Phys., 260 (2005), 131-146.
doi: 10.1007/s00220-005-1407-5. |
[12] |
I. Melbourne and M. Nicol, Large deviations for nonuniformly hyperbolic systems, Trans. Amer. Math. Soc., 360 (2000), 6661-6676.
doi: 10.1090/S0002-9947-08-04520-0. |
[13] |
S. Orei and S. Pelikan, Large deviations principles for stationary processes, Ann. Probab., 16 (1988), 1481-1495.
doi: 10.1214/aop/1176991579. |
[14] |
D. Ruelle, A measure associated with Axiom A attractors, Am. J. Math., 98 (1976), 619-654.
doi: 10.2307/2373810. |
[15] |
E. Rio, Théorie Asymptotique des Processus Aléatoires Faiblement Dépendants, Mathématiques & Applications(Berlin) [Mathematics and Applications] 31, Springer-Verlag, Berlin, 2000. |
[16] |
Ya. Sinai, Gibbs measure in ergodic theory, Russ. Math. Surv., 27 (1972), 21-64. |
[17] |
S. Waddington, Large deviations asymptotics for Anosov flows, Ann. Inst. H. Poincaré Anal. Non Linéaire, 13 (1996), 445-484. |
[18] |
L.-S. Young, Large deviations in dynamical systems, Trans. Amer. Math. Soc., 318 (1990), 525-543.
doi: 10.2307/2001318. |
[19] |
L.-S. Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. Math., 147 (1998), 585-650.
doi: 10.2307/120960. |
[20] |
L.-S. Young, Recurrence times and rates of mixing, Israel J. Math., 110 (1999), 153-188.
doi: 10.1007/BF02808180. |
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