Entropy via multiplicity

Boris Kruglikov; Martin Rypdal

doi:10.3934/dcds.2006.16.395

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2006, Volume 16, Issue 2: 395-410. Doi: 10.3934/dcds.2006.16.395

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Entropy via multiplicity

Boris Kruglikov^1, and
Martin Rypdal^1,

1.
Institute of Mathematics and Statistics, University of Troms∅, N-9037 Troms∅

Received: October 31, 2004

Revised: April 30, 2006

Published: March 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 37B40, 37D50; Secondary: 37D25, 37A35.

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