Real bounds, ergodicity and negative Schwarzian for multimodal maps

van Strien, Sebastian¹ ; Vargas, Edson²

¹ Department of Mathematics, Warwick University, Coventry CV4 7AL, England
² Department of Mathematics, University of São Paulo, São Paulo, Brazil

Journal of the American Mathematical Society, Tome 17 (2004) no. 4, pp. 749-782

Résumé

We consider smooth multimodal maps which have finitely many non-flat critical points. We prove the existence of real bounds. From this we obtain a new proof for the non-existence of wandering intervals, derive extremely useful improved Koebe principles, show that high iterates have ‘negative Schwarzian derivative’ and give results on ergodic properties of the map. One of the main complications in the proofs is that we allow $f$ to have inflection points.

Détail

DOI : 10.1090/S0894-0347-04-00463-1

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