Oriented local entropies for expansive actions by commuting automorphisms |
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Authors: | Vijay Chothi Graham Everest Thomas Ward |
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Affiliation: | 1. School of Mathematics, University of East Anglia, NR4 7TJ, Norwich, U.K.
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Abstract: | Given an expansive action α of ?2 by automorphisms of a compact connected metrizable abelian groupX, we show how the entropy of the action may be decomposed into local contributions, 1 $$h(alpha ) = sumlimits_{p leqslant infty } {h_p^{(a,b)} } (alpha )$$ in which the summandh p (a,b) (α) represents thep-adic entropy due to arithmetic or geometric hyperbolicity in the direction (a, b). We recognize thep-adic contribution as an integral over thep-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. |
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