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

M. A.O. Shinoda, Hiroki Takahasi

Research output: Contribution to journalArticle

Abstract

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
DOIs
Publication statusPublished - 2019 Jan 1

Fingerprint

Lyapunov
Optimization
Shift Map
Subset
Equilibrium State
Periodic Orbits
Orbits
Entropy
Interpolate
Perturbation
Interval
Theorem

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Lyapunov optimization for non-generic one-dimensional expanding Markov maps. / Shinoda, M. A.O.; Takahasi, Hiroki.

In: Ergodic Theory and Dynamical Systems, 01.01.2019.

Research output: Contribution to journalArticle

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