New York Journal of Mathematics
Volume 20 (2014) 431-439


Alireza Zamani Bahabadi

Asymptotic average shadowing property on nonuniformly expanding maps

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Published: April 15, 2014
Keywords: Asymptotic average shadowing property, δ-average-pseudo-orbit, transitivity, nonuniformly expanding
Subject: Primary: 54H20 Secondary: 54F99

In this paper, we investigate the relationships between asymptotic average shadowing property for nonuniformly expanding maps with some notions in dynamical systems. We prove that if nonuniformly expanding (NUE) map f has asymptotic average shadowing property (AASP), then f is transitive and weakly mixing. Finally as a remark we show that if the C2 diffeomorphism f is NUE and AASP then it has a unique SRB measure.

Author information

Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran