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piecewise monotonic map

Ergodic Theory and Dynamical Systems (1)

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Large deviation principle for piecewise monotonic maps with density of periodic measures
Part of
YONG MOO CHUNG, KENICHIRO YAMAMOTO
Journal:

Ergodic Theory and Dynamical Systems / Volume 43 / Issue 3 / March 2023

Published online by Cambridge University Press:

14 December 2021, pp. 861-872

Print publication:

March 2023
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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.