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arXiv · 1610.00822

Large deviation principle in one-dimensional dynamics

Yong Moo Chung·Juan Rivera-Letelier·Hiroki Takahasi
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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\nobreakdash-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.

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Yong Moo Chung, Juan Rivera-Letelier, Hiroki Takahasi. 2016-10-04. Large deviation principle in one-dimensional dynamics. https://arxiv.org/abs/1610.00822

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