Distortion estimates for planar diffeomorphisms

Sheldon Newhouse

doi:10.3934/dcds.2008.22.345

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2008, Volume 22, Issue 1&2: 345-412. Doi: 10.3934/dcds.2008.22.345

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Distortion estimates for planar diffeomorphisms

Sheldon Newhouse^1,

1.
Mathematics Department, Michigan State University, E. Lansing, MI 48824-1027

Received: June 30, 2007

Revised: October 31, 2007

Published: February 2008

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Abstract

We define new distortion quantities for diffeomorphisms of the Euclidean plane and study their properties. In particular, we obtain composition rules for these quantities analogous to standard rules for maps of an interval. Our results apply to maps with unbounded derivatives and have important applications in the theory of SRB measures for surface diffeomorphisms.

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Mathematics Subject Classification: Primary: 37C05, 37C40; Secondary: 37D05.

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