Hokkaido Mathematical Journal

HATOMOTO Jin,

Decay of correlations for some partially hyperbolic diffeomorphisms.

Hokkaido Mathematical Journal, 38 (2009) pp.39-65

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Abstract

In this paper we study a $C^{1+\alpha}$-partially hyperbolic diffeomorphism f of which restriction on one dimensional center unstable direction behaves as Manneville-Pomeau map. We show that f admits a unique ergodic SRB measure with polynomial upper bounds on correlations for Hölder continuous functions.

MSC(Primary)37A25
MSC(Secondary)37C40, 37D20
Uncontrolled Keywordsalmost Anosov diffeomophism, SRB measure, polynomial upper bounds on correlations, first return map.