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Entropy via multiplicity

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


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