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Stronger Lasota-Yorke inequality for one-dimensional piecewise expanding transformations


Authors: Peyman Eslami and Pawel Góra
Journal: Proc. Amer. Math. Soc. 141 (2013), 4249-4260
MSC (2010): Primary 37A10, 37A05, 37E05
Published electronically: August 6, 2013
MathSciNet review: 3105868
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Abstract: For a large class of piecewise expanding $ \mathcal {C}^{1,1}$ maps of the interval we prove the Lasota-Yorke inequality with a constant smaller than the previously known $ 2/\inf \vert\tau '\vert$. Consequently, the stability results of Keller-Liverani apply to this class and in particular to maps with periodic turning points. One of the applications is the stability of acim's for a class of W-shaped maps. Another application is an affirmative answer to a conjecture of Eslami-Misiurewicz regarding acim-stability of a family of unimodal maps.


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Additional Information

Peyman Eslami
Affiliation: Department of Mathematics & Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec, Canada H3G 1M8
Address at time of publication: Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma, Italy
Email: peslami@mathstat.concordia.ca, eslami@axp.mat.uniroma2.it

Pawel Góra
Affiliation: Department of Mathematics & Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec, Canada H3G 1M8
Email: pgora@mathstat.concordia.ca

DOI: https://doi.org/10.1090/S0002-9939-2013-11676-X
Received by editor(s): October 6, 2011
Received by editor(s) in revised form: January 7, 2012, and February 1, 2012
Published electronically: August 6, 2013
Additional Notes: The first author was supported by the INdAM-COFUND Marie Curie Fellowship during the final stages of the preparation of this article
Communicated by: Bryna Kra
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.