TY - JOUR
T1 - Large deviation principle in one-dimensional dynamics
AU - Chung, Yong Moo
AU - Rivera-Letelier, Juan
AU - Takahasi, Hiroki
N1 - Funding Information:
We would like to thank Michał Misiurewicz for his help with references, Bing Gao, Gerhard Keller and Masato Tsujii for fruitful discussions, and the anonymous referees for their healthy criticism that helped us improve the exposition in the introduction. The first-named author is partially supported by the Grant-in-Aid for Scientific Research (C) of the JSPS 16K05179. The second-named author is partially supported by FONDECYT Grant 1141091 and NSF Grant DMS-1700291. The last-named author is partially supported by the Grant-in-Aid for Young Scientists (A) of the JSPS 15H05435 and the Grant-in-Aid for Scientific Research (B) of the JSPS 16KT0021.
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00222-019-00899-w
DO - 10.1007/s00222-019-00899-w
M3 - Article
AN - SCOPUS:85069202401
SN - 0020-9910
VL - 218
SP - 853
EP - 888
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 3
ER -