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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Exponential mixing for skew products with discontinuities
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by Oliver Butterley and Peyman Eslami PDF
Trans. Amer. Math. Soc. 369 (2017), 783-803 Request permission

Abstract:

We consider the 2D skew product $F: (x,u) \mapsto (f(x), u+\tau (x))$, where the base map $f$ is a piecewise $\mathscr {C}^{2}$, covering and uniformly expanding the map of the circle, and the fibre map $\tau$ is piecewise $\mathscr {C}^{2}$. We show that this system mixes exponentially when $\tau$ is not cohomologous (via a Lipschitz function) to a piecewise constant.
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Additional Information
  • Oliver Butterley
  • Affiliation: Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
  • MR Author ID: 805760
  • Email: oliver.butterley@univie.ac.at
  • Peyman Eslami
  • Affiliation: Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma, Italy
  • MR Author ID: 819612
  • Email: eslami@mat.uniroma2.it
  • Received by editor(s): June 26, 2014
  • Received by editor(s) in revised form: January 22, 2015
  • Published electronically: May 6, 2016
  • Additional Notes: The first author was supported by the Austrian Science Fund, Lise Meitner position M1583.
    The second author was supported by an INdAM-COFUND Marie Curie fellowship
    This research was partially supported by the Stiftung Aktion Österreich Ungarn (AÖU), Projekt Nr. 87öu6.
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 783-803
  • MSC (2010): Primary 37A25; Secondary 37C30, 37D50
  • DOI: https://doi.org/10.1090/tran/6761
  • MathSciNet review: 3572254