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TOTALLY CHAIN-TRANSITIVE ATTRACTORS OF GENERIC HOMEOMORPHISMS ARE PERSISTENT

  • Published : 2005.08.01

Abstract

we prove that, given any compact metric space X, there exists a residual subset R of H(X), the space of all homeomorphisms on X, such that if $\in$ 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.

References

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Cited by

  1. Chain recurrence rates and topological entropy vol.156, pp.2, 2008, https://doi.org/10.1016/j.topol.2008.07.005