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Invariant measures for interval maps with different one-sided critical orders

Published online by Cambridge University Press:  28 August 2013

HONGFEI CUI  and
YIMING DING
HONGFEI CUI
Affiliation:
Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, PR China email cui@wipm.ac.cnding@wipm.ac.cn
YIMING DING
Affiliation:
Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, PR China email cui@wipm.ac.cnding@wipm.ac.cn
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Abstract

For an interval map whose critical point set may contain critical points with different one-sided critical orders and jump discontinuities, under a mild condition on critical orbits, we prove that it has an invariant probability measure which is absolutely continuous with respect to Lebesgue measure by using the methods of Bruin et al [Invent. Math. 172(3) (2008), 509–533], together with ideas from Nowicki and van Strien [Invent. Math. 105(1) (1991), 123–136]. We also show that it admits no wandering intervals.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 3 , May 2015 , pp. 835 - 853
Copyright
© Cambridge University Press, 2013 

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