On the Average Shadowing Property and Hyperbolicity

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New Zealand Journal of Mathematics

Vol. 42, (2012), Pages 189-194


Alireza Zamani Bahabadi

Department of Mathematics,

Ferdowsi University of Mashhad,

Mashhad,

Iran

mailto:zamany@um.ac.ir mailto:bahabadi@math.um.ac.ir






Abstract In this paper we show that there is a residual set R\subset Diff^1(M^3) such that if f\in R is tame and has the average shadowing property, then f is Anosov or there is a non-hyperbolic ergodic measure with support on the whole of the manifold M.

Keywords Average shadowing property, δ-average-pseudo-orbit, Dominated splitting, non hyperbolic ergodic measure.

Classification (MSC2000) 54H20: 37C05, 37C20, 37D25, 37D30.

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