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

M. A.O. Shinoda, Hiroki Takahasi

Research output: Contribution to journalArticle


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.

Original languageEnglish
JournalErgodic Theory and Dynamical Systems
Publication statusPublished - 2019 Jan 1


  • 2010 Mathematics Subject Classification
  • 37A40
  • 37C40
  • 37D05 (Secondary)
  • 37D35
  • 37E05 (Primary)

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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