Stronger Lasota-Yorke inequality for one-dimensional piecewise expanding transformations
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- by Peyman Eslami and Pawel Góra PDF
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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 $2/\inf |\tau ’|$. 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.References
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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
- MR Author ID: 819612
- 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
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 4249-4260
- MSC (2010): Primary 37A10, 37A05, 37E05
- DOI: https://doi.org/10.1090/S0002-9939-2013-11676-X
- MathSciNet review: 3105868