Oriented local entropies for expansive actions by commuting automorphisms

Chothi, Vijay, Everest, Graham and Ward, Tom (1996) Oriented local entropies for expansive actions by commuting automorphisms. Israel Journal of Mathematics, 93 (1). pp. 281-301. ISSN 0021-2172

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Given an expansive action a of Z2 by automorphisms of a compact connected metrizable abelian group X, we show how the entropy of the action may be decomposed into local contributions, h(a) = å p £ ¥ hp(a,b)(a) (1) in which the summand hp(a,b)(a) represents the p-adic entropy due to arithmetic or geometric hyperbolicity in the direction (a,b). We recognize the p-adic contribution as an integral over the p-adic unit circle, in analogy with the global counterpart. As (a,b) changes, the decomposition (1) changes only when the line through (a,b) passes through one of a finite collection of critical directions, which are explicitly identified.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:48
Last Modified: 15 Dec 2022 02:04
URI: https://ueaeprints.uea.ac.uk/id/eprint/18600
DOI: 10.1007/BF02761107

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