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An area approach to wandering domains for smooth surface endomorphisms

Published online by Cambridge University Press:  19 September 2008

Alec Norton
Alec Norton
Affiliation:
Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA
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Abstract

We prove an infinite-area lemma for maps which are area non-contracting on the boundaries of certain domains; the maps are required to be smooth to the extent that their Jacobians are twice differentiable (see Main Lemma below). It will follow that a hyperbolic rational map has no wandering simply connected domains. As a more direct corollary, a C3 diffeomorphism f of a compact smooth 2-manifold cannot have a wandering domain Δ if f is area non-contracting on the boundary of each forward image of Δ.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 1 , March 1991 , pp. 181 - 187
Copyright
Copyright © Cambridge University Press 1991

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References

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