A local variational principle for the topological entropy

PIERRE-PAUL ROMAGNOLI

doi:10.1017/S0143385703000105

Abstract

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In this paper we introduce two notions of measure-theoretical entropy for covers and one notion of topological entropy for open covers. These notions extend the classical concept of measure-theoretical entropy of measurable partitions to measurable covers. Using these notions we prove a local variational principle for any given open cover.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Downarowicz, Tomasz 2005. Entropy structure. Journal d'Analyse Mathématique, Vol. 96, Issue. 1, p. 57.

Ye, Xiangdong and Zhang, Guohua 2007. Entropy points and applications. Transactions of the American Mathematical Society, Vol. 359, Issue. 12, p. 6167.

Shapira, Uri 2007. Measure theoretical entropy of covers. Israel Journal of Mathematics, Vol. 158, Issue. 1, p. 225.

Huang, Wen Ye, Xiangdong and Zhang, Guohua 2007. Relative entropy tuples, relative u.p.e. and c.p.e. extensions. Israel Journal of Mathematics, Vol. 158, Issue. 1, p. 249.

Huang, Wen and Yi, Yingfei 2007. A local variational principle of pressure and its applications to equilibrium states. Israel Journal of Mathematics, Vol. 161, Issue. 1, p. 29.

Huang, Wen 2008. Stable Sets and $$\epsilon$$ -Stable Sets in Positive-Entropy Systems. Communications in Mathematical Physics, Vol. 279, Issue. 2, p. 535.

GLASNER, ELI and YE, XIANGDONG 2009. Local entropy theory. Ergodic Theory and Dynamical Systems, Vol. 29, Issue. 2, p. 321.

Kerr, David and Li, Hanfeng 2009. Combinatorial independence in measurable dynamics. Journal of Functional Analysis, Vol. 256, Issue. 5, p. 1341.

Chen, Beimei Ding, Bangfeng and Cao, Yongluo 2010. The local variational principle of topological pressure for sub-additive potentials. Nonlinear Analysis: Theory, Methods & Applications, Vol. 73, Issue. 11, p. 3525.

Cheng, Wen-Chiao and Li, Bing 2010. Zero Entropy Systems. Journal of Statistical Physics, Vol. 140, Issue. 5, p. 1006.

Ma, XianFeng Chen, ErCai and Zhang, AiHua 2010. A relative local variational principle for topological pressure. Science China Mathematics, Vol. 53, Issue. 6, p. 1491.

Huang, Wen Ye, Xiangdong and Zhang, Guohua 2011. Local entropy theory for a countable discrete amenable group action. Journal of Functional Analysis, Vol. 261, Issue. 4, p. 1028.

Huang, Wen Lu, Ping and Ye, Xiangdong 2011. Measure-theoretical sensitivity and equicontinuity. Israel Journal of Mathematics, Vol. 183, Issue. 1, p. 233.

LI, YUAN CHEN, ERCAI and CHENG, WEN-CHIAO 2012. Tail pressure and the tail entropy function. Ergodic Theory and Dynamical Systems, Vol. 32, Issue. 4, p. 1400.

Li, Yuan Chen, Ercai and Cheng, Wen-Chiao 2012. Variational inequality for conditional pressure on a Borel subset. Pacific Journal of Mathematics, Vol. 256, Issue. 1, p. 151.

Zhang, GuoHua 2012. Relativization of dynamical properties. Science China Mathematics, Vol. 55, Issue. 5, p. 913.

Zhang, Guohua 2012. Local variational principle concerning entropy of a sofic group action. Journal of Functional Analysis, Vol. 262, Issue. 4, p. 1954.

Yan, Kesong 2013. Sub-Additive and Asymptotically Sub-Additive Topological Pressure for $$\mathbb{Z }^d$$ -Actions. Journal of Dynamics and Differential Equations, Vol. 25, Issue. 3, p. 653.

MA, XIANFENG and CHEN, ERCAI 2013. A LOCAL VARIATIONAL PRINCIPLE FOR RANDOM BUNDLE TRANSFORMATIONS. Stochastics and Dynamics, Vol. 13, Issue. 03, p. 1250023.

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A local variational principle for the topological entropy

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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A local variational principle for the topological entropy

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