Totally chain-transitive attractors of generic homeomorphisms are persistent
Bull. Korean Math. Soc. 2005 Vol. 42, No. 3, 631-638
Printed September 1, 2005
Fatemeh Helen Ghane and Abbas Fakhari
Ferdowsi University of Mashhad, Ferdowsi University of Mashhad
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
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