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
- weak rank one
- shadowing
- Markov diagram
- strongly positive recurrent Markov shifts
- kneading invariants
- Artin-Mazur zeta function
- periodic orbits
- measures maximizing entropy
- horseshoes
- piecewise monotone maps
- interval maps
- variational principle
- entropy
- symbolic dynamics
- ergodic theory
- topological and combinatorial dynamics
Domaines
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