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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Viana maps driven by Benedicks-Carleson quadratic maps
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by Rui Gao PDF
Trans. Amer. Math. Soc. 374 (2021), 1449-1495 Request permission


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
  • ORCID: 0000-0001-6770-5927
  • Email:
  • 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).
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 374 (2021), 1449-1495
  • MSC (2020): Primary 37C40, 37D25; Secondary 37E05, 37F10
  • DOI:
  • MathSciNet review: 4196399