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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Viana maps driven by Benedicks-Carleson quadratic maps


Author: Rui Gao
Journal: Trans. Amer. Math. Soc. 374 (2021), 1449-1495
MSC (2020): Primary 37C40, 37D25; Secondary 37E05, 37F10
DOI: https://doi.org/10.1090/tran/8249
Published electronically: December 3, 2020
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Abstract: We study the measurable dynamics of a family of skew-product maps known as Viana maps. In our setting, those maps are constructed by coupling two quadratic maps, and we aim at showing the abundance of non-uniform hyperbolicity in this family. We prove that, for any polynomial coupling function of odd degree, when the parameter pair of the two factor quadratic maps is chosen from a two-dimensional positive measure set, the associated Viana map has two positive Lyapunov exponents and admit finitely many ergodic absolutely continuous invariant probability measures.


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Additional Information

Rui Gao
Affiliation: College of Mathematics, Sichuan University, Chengdu 610064, People’s Republic of China
Email: gaoruimath@scu.edu.cn

DOI: https://doi.org/10.1090/tran/8249
Received by editor(s): June 18, 2018
Received by editor(s) in revised form: July 9, 2020
Published electronically: December 3, 2020
Additional Notes: This work was partially supported by NSFC (No. 11701394).
Article copyright: © Copyright 2020 American Mathematical Society