Complexity and directional entropy in two dimensions

Ryan Broderick; Van Cyr; Bryna Kra

doi:10.1007/s11856-016-1376-8

Complexity and directional entropy in two dimensions

Ryan Broderick^*, Van Cyr, Bryna Kra

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study the directional entropy of a dynamical system associated to a Z² configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some direction is periodic. In particular, we show that all nonexpansive directions in a Z² system with the same local assumptions have zero directional entropy.

Original language	English (US)
Pages (from-to)	135-162
Number of pages	28
Journal	Israel Journal of Mathematics
Volume	215
Issue number	1
DOIs	https://doi.org/10.1007/s11856-016-1376-8
State	Published - Sep 1 2016

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Mathematics(all)

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10.1007/s11856-016-1376-8

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title = "Complexity and directional entropy in two dimensions",

abstract = "We study the directional entropy of a dynamical system associated to a Z2 configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some direction is periodic. In particular, we show that all nonexpansive directions in a Z2 system with the same local assumptions have zero directional entropy.",

author = "Ryan Broderick and Van Cyr and Bryna Kra",

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AU - Kra, Bryna

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N2 - We study the directional entropy of a dynamical system associated to a Z2 configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some direction is periodic. In particular, we show that all nonexpansive directions in a Z2 system with the same local assumptions have zero directional entropy.

AB - We study the directional entropy of a dynamical system associated to a Z2 configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some direction is periodic. In particular, we show that all nonexpansive directions in a Z2 system with the same local assumptions have zero directional entropy.

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Complexity and directional entropy in two dimensions

Abstract

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