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February  2008, 22(1&2): 345-412. doi: 10.3934/dcds.2008.22.345

Distortion estimates for planar diffeomorphisms

Sheldon Newhouse 1,

1. 

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

Received  July 2007 Revised  November 2007 Published  June 2008

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.
Keywords: parabolic, planar maps, SRB measures., hyperbolic, distortion.
Mathematics Subject Classification: Primary: 37C05, 37C40; Secondary: 37D0.
Citation: Sheldon Newhouse. Distortion estimates for planar diffeomorphisms. Discrete & Continuous Dynamical Systems, 2008, 22 (1&2) : 345-412. doi: 10.3934/dcds.2008.22.345
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