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Large deviation principle for piecewise monotonic maps with density of periodic measures

Part of: Ergodic theory Low-dimensional dynamical systems Limit theorems Topological dynamics

Published online by Cambridge University Press:  14 December 2021

YONG MOO CHUNG  and
KENICHIRO YAMAMOTO
YONG MOO CHUNG
Affiliation:
Department of Applied Mathematics, Hiroshima University, Higashi-Hiroshima 739-8527, Japan (e-mail: chung@amath.hiroshima-u.ac.jp)
KENICHIRO YAMAMOTO*
Affiliation:
Department of General Education, Nagaoka University of Technology, Nagaoka 940-2188, Japan
*
e-mail: k_yamamoto@vos.nagaokaut.ac.jp
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Abstract

We show that a piecewise monotonic map with positive topological entropy satisfies the level-2 large deviation principle with respect to the unique measure of maximal entropy under the conditions that the corresponding Markov diagram is irreducible and that the periodic measures of the map are dense in the set of ergodic measures. This result can apply to a broad class of piecewise monotonic maps, such as monotonic mod one transformations and piecewise monotonic maps with two monotonic pieces.

Keywords

large deviationpiecewise monotonic mapperiodic measure

MSC classification

Primary: 37A50: Relations with probability theory and stochastic processes 37E05: Maps of the interval (piecewise continuous, continuous, smooth) 37B10: Symbolic dynamics
Secondary: 60F10: Large deviations
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 43 , Issue 3 , March 2023 , pp. 861 - 872
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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