Open AccessReal bounds, ergodicity and negative Schwarzian for multimodal maps
Author(s) -
S Van Strien,
Edson Vargas
Publication year - 2004
Publication title -
journal of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 8.574
H-Index - 111
eISSN - 1088-6834
pISSN - 0894-0347
DOI - 10.1090/s0894-0347-04-00463-1
Subject(s) - ergodic theory , mathematics , ergodicity , iterated function , inflection point , semantics (computer science) , mathematical proof , algorithm , pure mathematics , computer science , mathematical analysis , statistics , geometry , programming language
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 f to have inflection points.