No bounded geometry wandering domains for sufficiently regular automorphisms

A question whether sufficiently regular manifold automorphisms may have wandering domains with controlled geometry is answered in the negative for quasiconformal or smooth homeomorphisms of n n -tori, n ≥ 2 n\ge 2 , and hyperbolic surfaces. Besides control on geometry of wandering domains, the assum...

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Veröffentlicht in:	Transactions of the American Mathematical Society 2024-10
1. Verfasser:	Merenkov, Sergei
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Sprache:	eng
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creator	Merenkov, Sergei
description	A question whether sufficiently regular manifold automorphisms may have wandering domains with controlled geometry is answered in the negative for quasiconformal or smooth homeomorphisms of n n -tori, n ≥ 2 n\ge 2 , and hyperbolic surfaces. Besides control on geometry of wandering domains, the assumptions are either analytic, e.g., minimal sets having measure zero or supporting invariant conformal structures, or geometric, such as uniform relative separation of wandering domains.
doi_str_mv	10.1090/tran/9281
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title	No bounded geometry wandering domains for sufficiently regular automorphisms
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