A minicourse on entropy theory on the interval
Résumé
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.
Mots clés
topological and combinatorial dynamics
ergodic theory
symbolic dynamics
entropy
variational principle
interval maps
piecewise monotone maps
horseshoes
measures maximizing entropy
periodic orbits
Artin-Mazur zeta function
kneading invariants
strongly positive recurrent Markov shifts
Markov diagram
shadowing
weak rank one
Domaines
Systèmes dynamiques [math.DS]
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