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June  2006, 16(2): 395-410. doi: 10.3934/dcds.2006.16.395

Entropy via multiplicity

Boris Kruglikov 1, and  Martin Rypdal 1,

1. 

Institute of Mathematics and Statistics, University of Troms∅, N-9037 Troms∅

Received  November 2004 Revised  May 2006 Published  July 2006

The topological entropy of piecewise affine maps is studied. It is shown that singularities may contribute to the entropy only if there is angular expansion and we bound the entropy via the expansion rates of the map. As a corollary, we deduce that non-expanding conformal piecewise affine maps have zero topological entropy. We estimate the entropy of piecewise affine skew-products. Examples of abnormal entropy growth are provided.
Keywords: entropy, spherization, skew-product, Piecewise affine maps, multiplicity, singularities, angular expansion..
Mathematics Subject Classification: Primary: 37B40, 37D50; Secondary: 37D25, 37A3.
Citation: Boris Kruglikov, Martin Rypdal. Entropy via multiplicity. Discrete & Continuous Dynamical Systems - A, 2006, 16 (2) : 395-410. doi: 10.3934/dcds.2006.16.395
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