A minicourse on entropy theory on the interval

2006/11/11 by Jérôme Buzzi, Buzzi, Jerome
Mathematics · #37A35 #37B10 #37E05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · doi:10.48550/arxiv.math/0611337

openalex publication_date 2006/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a survey of the entropy theory of interval maps as it can be analyzed using ergodic theory, especially measures of maximum entropy and periodic points. The main tools are (i) a version of Hofbauer's Markov diagram, (ii) the shadowing property and the implied entropy bound and weak rank one property, (iii) strongly positively recurrent countable state Markov shifts. Proofs are given for selected results. This article is based on the lectures given at the Ecole thematique de theorie ergodique at the C.I.R.M., Marseilles, in April 2006.

Citations

• Dimension, entropy and Lyapunov exponents
• Entropy via multiplicity

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