Lyapunov optimization for non-generic one-dimensional expanding Markov maps

Mao Shinoda, Hiroki Takahasi

研究成果: Article査読

1 被引用数 (Scopus)

抄録

For a non-generic, yet dense subset of expanding Markov maps of the interval we prove the existence of uncountably many Lyapunov optimizing measures which are ergodic, fully supported and have positive entropy. These measures are equilibrium states for some Hölder continuous potentials. We also prove the existence of another non-generic dense subset for which the optimizing measure is unique and supported on a periodic orbit. A key ingredient is a new perturbation theorem which allows us to interpolate between expanding Markov maps and the shift map on a finite number of symbols.

本文言語English
ページ(範囲)2571-2592
ページ数22
ジャーナルErgodic Theory and Dynamical Systems
40
9
DOI
出版ステータスPublished - 2020 9 1

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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