From Zero to Positive Entropy

2022/04/14 by Sylvain Crovisier, Enrique Pujals · 2 citations
Social Sciences · #Interdisciplinary Cultural and Social Studies #Sociology and Norbert Elias #Social and Cultural Dynamics

paper · pdf · doi:10.1090/noti2478

Abstract

A tentative global framework toward describing a large class of two-dimensional dynamics, inspired partially by the developments in the one-dimensional theory of interval maps, is discussed. More precisely, we present a class of intermediate smooth dynamics between one and higher dimensions.

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• The boundary of chaos for piecewise smooth maps and the boundary of positive Hausdorff dimension for survivor sets of open maps
• Average measure theoretic entropy for a family of expanding on average random Blaschke products

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