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Attractors of dissipative homeomorphisms of the infinite surface homeomorphic to a punctured sphere

    https://doi.org/10.1142/S0219199722500109Cited by:0 (Source: Crossref)

    A class of dissipative orientation preserving homeomorphisms of the infinite annulus, pairs of pants, or generally any infinite surface homeomorphic to a punctured sphere is considered. We prove that in some isotopy classes the local behavior of such homeomorphisms at a fixed point, namely the existence of so-called inverse saddle, impacts the topology of the attractor — it cannot be arcwise connected.

    AMSC: 37E30, 37C25