Large deviation principle in one-dimensional dynamics

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.

26 pages, 2 figures, Inventiones mathematicae, to appear

References in corpus (2)

• Chaos on the interval - a survey of relationship between the various kinds of chaos for continuous interval maps
• Large Deviation Principle for $S$-unimodal maps with flat critical point

Cited by in corpus (1)

• Large Deviation Principle for $S$-unimodal maps with flat critical point