Large deviation principle in one-dimensional dynamics

• 成果类型: Article
• 署名作者: Chung, Yong Moo; Rivera-Letelier, Juan; Takahasi, Hiroki
• 署名单位: Hiroshima University; University of Rochester; Keio University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00899-w
• 发表日期: 2019
• 页码: 853-888
• 关键词: backward stability; MAPS; HYPERBOLICITY; families; systems

摘要

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.