Totally chain-transitive attractors of generic homeomorphisms are persistent

Fatemeh Helen Ghane; Abbas Fakhari

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Bull. Korean Math. Soc. 2005; 42(3): 631-638

Printed September 1, 2005

Totally chain-transitive attractors of generic homeomorphisms are persistent

Fatemeh Helen Ghane and Abbas Fakhari

Ferdowsi University of Mashhad, Ferdowsi University of Mashhad

Abstract

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Abstract

we prove that, given any compact metric space $X$, there exists a residual subset $\mathcal{R}$ of ${\mathcal{H }}(X)$, the space of all homeomorphisms on $X$, such that if $f\in\mathcal{R}$ has a totally chain-transitive attractor A, then any g sufficiently close to f has a totally chain-transitive attractor $A_g$ which is convergent to $A$ in the Hausdorff topology.

Keywords: totally chain-transitive, attractor, persistent

MSC numbers: 37B20, 37C70, 54H20