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  Far East Journal of Mathematical Sciences (FJMS)  
 ISSN: 0972-0871
 
 
 

     Far East Journal of Mathematical Sciences (FJMS)
    Volume 33, Issue 2, Pages 207 - 235 (May 2009)


MIXING RATES FOR DISCRETE DYNAMICAL SYSTEMS WITH WEAK HYPERBOLIC PRODUCT STRUCTURE

Jin Hatomoto (Japan)

Received February 11, 2009

References:



[1] M. Benedicks and L.-S. Young, Markov extensions and decay of correlations for certain Hénon maps, Astérisque 261 (2000), 13-56.

[2] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Springer Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin, New York, 1975.

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

[4] J. Buzzi and V. Maume-Deschamps, Decay of correlations on towers with non-Hölder Jacobian and non-exponential return time, Discrete Contin. Dyn. Syst. 12(4) (2005), 639-656.

[5] A. A. Castro, Backward inducing and exponential decay of correlations for partially hyperbolic attractors, Israel J. Math. 130 (2002), 29-75.

[6] A. A. Castro, Fast mixing for attractors with mostly contracting central direction, Ergo. Theo. Dynam. Sys. 24 (2004), 17-44.

[7] J. Hatomoto, Diffeomorphisms admitting SRB measures and their regularity, Kodai Math. J. 29 (2006), 211-226.

[8] J. Hatomoto, Mixing properties for invertible maps with weak hyperbolic product structure, Far East J. Math. Sci. (FJMS) 29(2) (2008), 257-310.

[9] J. Hatomoto, Central limit theorem for invertible maps with weak hyperbolic product structure, Far East J. Math. Sci. (FJMS) 29(3) (2008), 729-752.

[10] J. Hatomoto, Fast mixing of weak hyperbolic product structure, Far East J. Math. Sci. (FJMS) 30(3) (2008), 537-546.

[11] J. Hatomoto, Decay of correlations for some partially hyperbolic diffeomorphisms, Hokkaido Math. J. (to appear).

[12] H. Hu, Conditions for the existence of SBR measures for “almost Anosov” diffeomorphisms, Trans. Amer. Math. Soc. 5 (1999), 2331-2367.

[13] V. Maume-Deschamps, Projective metrics and mixing properties on towers, Trans. Amer. Math. Soc. 353(8) (2001), 3371-3389.

[14] D. Ruelle, A measure associated with axiom-A attractors, Amer. J. Math. 98(3) (1976), 619-654.

[15] Ya. G. Sinai, Gibbs measures in ergodic theory, Uspehi Mat. Nauk 27 (1972), 21-64.

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

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

Keywords and phrases: decay of correlation functions, weak hyperbolic product structure, SRB measure.

 


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