Positive entropies and horseshoes in infinite dimensional dynamics via an approach of plaque family

Chun Fang, Mats Anders Gideon Gyllenberg, Dawei Yang

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We study the smooth ergodic theory for C1 mappings of a separated Banach space with C1 bump function. Suppose the system has positive entropy, we show that the horseshoe present with the assumption of domination. This result generalized Katok's famous result on positive entropy implying chaos to Banach spaces. The method we used in this paper is base on an infinite dimensional version of Plaque Family Theorem.
Original languageEnglish
JournalJournal of Functional Analysis
Publication statusIn preparation - 2015
MoE publication typeA1 Journal article-refereed

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