Large deviation principle in one-dimensional dynamics

Yong Moo Chung, Juan Rivera-Letelier, Hiroki Takahasi

Research output: Contribution to journalArticle

Abstract

We study the dynamics of smooth interval maps with non-flat critical points. For every such a map that is topologically exact, we establish the full (level-2) Large Deviation Principle for empirical means. In particular, the Large Deviation Principle holds for every non-renormalizable quadratic map. This includes the maps without physical measure found by Hofbauer and Keller, and challenges the widely-shared view of the Large Deviation Principle as a refinement of laws of large numbers.

Original languageEnglish
Pages (from-to)853-888
Number of pages36
JournalInventiones Mathematicae
Volume218
Issue number3
DOIs
Publication statusPublished - 2019 Dec 1

ASJC Scopus subject areas

  • Mathematics(all)

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