Volume growth and entropy |
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Authors: | Y Yomdin |
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Institution: | (1) Department of Mathematics, Ben Gurion Univesity of the Negev, 84105 Beer Sheva, Israel |
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Abstract: | An inequality is proved, bounding the growth rates of the volumes of iterates of smooth submanifolds in terms of the topological
entropy. ForC
x-smooth mappings this inequality implies the entropy conjecture, and, together with the opposite inequality, obtained by S.
Newhouse, proves the coincidence of the growth rate of volumes and the topological entropy, as well as the upper semicontinuity
of the entropy. |
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Keywords: | |
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