Markov structures and decay of correlations for non-uniformly expanding dynamical systems

Alves, José F.; Luzzatto, Stefano; Pinheiro, Vilton

doi:10.1016/j.anihpc.2004.12.002

Alves, José F. ; Luzzatto, Stefano ; Pinheiro, Vilton

Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 6, pp. 817-839.

MR Zbl | 6 citations dans Numdam

DOI : 10.1016/j.anihpc.2004.12.002

@article{AIHPC_2005__22_6_817_0,
     author = {Alves, Jos\'e F. and Luzzatto, Stefano and Pinheiro, Vilton},
     title = {Markov structures and decay of correlations for non-uniformly expanding dynamical systems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {817--839},
     publisher = {Elsevier},
     volume = {22},
     number = {6},
     year = {2005},
     doi = {10.1016/j.anihpc.2004.12.002},
     mrnumber = {2172861},
     zbl = {02245288},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2004.12.002/}
}

TY  - JOUR
AU  - Alves, José F.
AU  - Luzzatto, Stefano
AU  - Pinheiro, Vilton
TI  - Markov structures and decay of correlations for non-uniformly expanding dynamical systems
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2005
SP  - 817
EP  - 839
VL  - 22
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2004.12.002/
DO  - 10.1016/j.anihpc.2004.12.002
LA  - en
ID  - AIHPC_2005__22_6_817_0
ER  -

%0 Journal Article
%A Alves, José F.
%A Luzzatto, Stefano
%A Pinheiro, Vilton
%T Markov structures and decay of correlations for non-uniformly expanding dynamical systems
%J Annales de l'I.H.P. Analyse non linéaire
%D 2005
%P 817-839
%V 22
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2004.12.002/
%R 10.1016/j.anihpc.2004.12.002
%G en
%F AIHPC_2005__22_6_817_0

Alves, José F.; Luzzatto, Stefano; Pinheiro, Vilton. Markov structures and decay of correlations for non-uniformly expanding dynamical systems. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 6, pp. 817-839. doi : 10.1016/j.anihpc.2004.12.002. http://www.numdam.org/articles/10.1016/j.anihpc.2004.12.002/

Bibliographie
Cité par

[1] Alves J.F., SRB measures for non-hyperbolic systems with multidimensional expansion, Ann. Sci. École Norm. Sup. 33 (4) (2000) 1-32. | Numdam | MR | Zbl

[2] Alves J.F., Araújo V., Random perturbations of nonuniformly expanding maps, Astérisque 286 (2003) 25-62. | Numdam | MR | Zbl

[3] Alves J.F., Bonatti C., Viana M., SRB measures for partially hyperbolic systems whose central direction is mostly expanding, Invent. Math. 140 (2000) 351-398. | MR | Zbl

[4] Alves J.F., Luzzatto S., Pinheiro V., Lyapunov exponent and rates of mixing for one-dimensional maps, Ergodic Theory Dynam. Systems 24 (2004) 637-657. | MR | Zbl

[5] Alves J.F., Viana M., Statistical stability for robust classes of maps with non-uniform expansion, Ergodic Theory Dynam. Systems 22 (2002) 1-32. | MR | Zbl

[6] Adler R., Weiss B., Proc. Entropy, a complete metric invariant for automorphisms of the torus, Nat. Acad. Sci. USA 57 (1967) 1573-1576. | MR | Zbl

[7] Adler R., Weiss B., Similarity of Automorphisms of the Torus, Mem. Amer. Math. Soc., vol. 98, Amer. Math. Soc., Providence, RI, 1970. | MR | Zbl

[8] V. Baladi, M. Benedicks, V. Maume-Deschamps, Almost sure rate of mixing for i.i.d unimodal maps, Ann. Sci. Écol. Norm. Sup. (4) (2002). | Numdam | MR | Zbl

[9] Bruin H., Luzzatto S., Van Strien S., Rates of decay of correlations in one-dimensional dynamics, Ann. Sci. Écol. Norm. Sup. 36 (2003) 621-646. | Numdam | MR | Zbl

[10] Bowen R., Ruelle D., The ergodic theory of Axiom A flows, Invent. Math. 29 (1975) 181-202. | MR | Zbl

[11] Bowen R., Markov partitions for Axiom diffeomorphisms, Amer. J. Math. 92 (1970) 725-747. | MR | Zbl

[12] Bowen R., Equilibrium States and the Ergodic Theory of Axiom A Diffeomorphisms, Lecture Notes in Math., vol. 92, Springer, 1975. | MR | Zbl

[13] Bressaud X., Subshifts on an infinite alphabet, Ergodic Theory Dynam. Systems 19 (5) (1999) 1175-1200. | MR | Zbl

[14] Bunimovich L.A., Sinaĭ Ya.G., Chernov N.I., Statistical properties of two-dimensional hyperbolic billiards, Russian Math. Surveys 46 (4) (1991) 47-106. | MR | Zbl

[15] Buzzi J., Markov extensions for multi-dimensional dynamical systems, Israel J. Math. 112 (1999) 357-380. | MR | Zbl

[16] Buzzi J., Maume-Deschamps V., Decay of correlations for piecewise invertible maps in higher dimensions, Israel J. Math. 131 (2002) 203-220. | MR | Zbl

[17] J. Buzzi, V. Maume-Deschamps, Decay of correlations on towers with non-Hólder Jacobian and non-exponential return time, Preprint, 2002. | MR

[18] Buzzi J., Sester O., Tsujii M., Weakly expanding skew-products of quadratic maps, Ergodic Theory Dynam. Systems 24 (2004) 385-405. | MR | Zbl

[19] M. Holland, Slowly mixing systems and intermittency maps, Ergodic Theory Dynam. Systems, in press. | MR | Zbl

[20] Hu H., Decay of correlations for piecewise smooth maps with indifferent fixed points, Ergodic Theory Dynam. Systems 24 (2004) 495-524. | MR | Zbl

[21] Krüger T., Troubetzkoy S., Markov partitions and shadowing for non-uniformly hyperbolic systems with singularitie, Ergodic Theory Dynam. Systems 12 (3) (1992) 487-508. | MR | Zbl

[22] Liverani C., Saussol B., Vaienti S., A probabilistic approach to intermittancy, Ergodic Theory Dynam. Systems 19 (1999) 671-685. | MR | Zbl

[23] Maume-Deschamps V., Correlation decay for Markov maps on a countable state space, Ergodic Theory Dynam. Systems 21 (2001) 165-196. | MR | Zbl

[24] Pollicott M., Yuri M., Statistical properties of maps with indifferent periodic points, Commun. Math. Phys. 217 (2001) 503-520. | MR | Zbl

[25] Sarig O., Thermodynamical formalism for countable Markov shifts, Ergodic Theory Dynam. Systems 19 (1999) 1565-1593. | MR | Zbl

[26] Sarig O., Subexponential decay of correlations, Invent. Math. 150 (2002) 629-653. | MR | Zbl

[27] Sinai Y., Markov partitions and U-diffeomorphisms, Funktsional Anal. i Prilozhen. 32 (2) (1968) 70-80. | MR | Zbl

[28] Viana M., Multidimensional non-hyperbolic attractors, Publ. Math. IHES 85 (1997) 63-96. | Numdam | Zbl

[29] Young L.-S., Statistical properties of dynamical systems with some hyperbolicity, Ann. Math. 147 (1998) 585-650. | MR | Zbl

[30] Young L.-S., Recurrence times and rates of mixing, Israel J. Math. 110 (1999) 153-188. | MR | Zbl

[31] Yuri M., On the speed of convergence to equilibrium states for multi-dimensional maps with indifferent fixed points, Nonlinearity 15 (2002) 429-445. | MR | Zbl

Cité par Sources :