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

Published online by Cambridge University Press:  14 December 2021

YONG MOO CHUNG
Affiliation:
Department of Applied Mathematics, Hiroshima University, Higashi-Hiroshima739-8527, Japan (e-mail: chung@amath.hiroshima-u.ac.jp)
KENICHIRO YAMAMOTO*
Affiliation:
Department of General Education, Nagaoka University of Technology, Nagaoka940-2188, Japan

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.

Type
Original Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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