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January, 2022 Large deviation principle for $S$-unimodal maps with flat critical points
Yong Moo CHUNG, Hiroki TAKAHASI
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J. Math. Soc. Japan 74(1): 129-150 (January, 2022). DOI: 10.2969/jmsj/85138513

Abstract

We study a topologically exact, negative Schwarzian unimodal map without neutral periodic points whose critical point is non-recurrent and flat. Assuming that the critical order is polynomial or logarithmic, we establish the large deviation principle and provide a partial description of the minimizers of the rate function. We apply our main results to a certain parametrized family of unimodal maps in the same topological conjugacy class, and determine the sets of minimizers.

Funding Statement

The first author was supported by the JSPS KAKENHI 20K03631. The second author was supported by the JSPS KAKENHI 19K21835, 20H01811.

Citation

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Yong Moo CHUNG. Hiroki TAKAHASI. "Large deviation principle for $S$-unimodal maps with flat critical points." J. Math. Soc. Japan 74 (1) 129 - 150, January, 2022. https://doi.org/10.2969/jmsj/85138513

Information

Received: 7 July 2020; Published: January, 2022
First available in Project Euclid: 22 June 2021

Digital Object Identifier: 10.2969/jmsj/85138513

Subjects:
Primary: 37E05
Secondary: 37A50 , 37C40 , 37D35 , 60F10

Keywords: flat critical point , large deviation principle , unimodal map

Rights: Copyright ©2022 Mathematical Society of Japan

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Vol.74 • No. 1 • January, 2022
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