A minicourse on entropy theory on the interval

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.