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Exponential mixing for skew products with discontinuities


Authors: Oliver Butterley and Peyman Eslami
Journal: Trans. Amer. Math. Soc. 369 (2017), 783-803
MSC (2010): Primary 37A25; Secondary 37C30, 37D50
DOI: https://doi.org/10.1090/tran/6761
Published electronically: May 6, 2016
MathSciNet review: 3572254
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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
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
Email: eslami@mat.uniroma2.it

DOI: https://doi.org/10.1090/tran/6761
Keywords: Exponential mixing, skew product, oscillatory cancellation, transfer operator, partially hyperbolic
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.
Article copyright: © Copyright 2016 American Mathematical Society