Large deviation principle in one-dimensional dynamics

Large deviation principle in one-dimensional dynamics

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....

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Veröffentlicht in:Inventiones mathematicae 2019-12, Vol.218 (3), p.853-888
Hauptverfasser: Chung, Yong Moo, Rivera-Letelier, Juan, Takahasi, Hiroki
Format: Artikel
Sprache:eng
Schlagworte:
Critical point
Deviation
Fractals
Mathematics
Mathematics and Statistics
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Zusammenfassung: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.
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-019-00899-w