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Skew product attractors and concavity


Authors: Lluís Alsedà and Michał Misiurewicz
Journal: Proc. Amer. Math. Soc. 143 (2015), 703-716
MSC (2010): Primary 37C55, 37C70
Published electronically: October 3, 2014
MathSciNet review: 3283657
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Abstract: We propose an approach to the attractors of skew products that tries to avoid unnecessary structures on the base space and rejects the assumption on the invariance of an attractor. When nonivertible maps in the base are allowed, one can encounter the mystery of the vanishing attractor. In the second part of the paper, we show that if the fiber maps are concave interval maps, then contraction in the fibers does not depend on the map in the base.


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Lluís Alsedà
Affiliation: Departament de Matemàtiques, Edifici Cc, Universitat Autònoma de Barcelona, 08913 Cerdanyola del Vallès, Barcelona, Spain
Email: alseda@mat.uab.cat

Michał Misiurewicz
Affiliation: Department of Mathematical Sciences, Indiana University–Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, Indiana 46202
Email: mmisiure@math.iupui.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12271-4
Keywords: Skew product, attractor, quasiperiodic forcing, concavity, monotonicity
Received by editor(s): July 16, 2012
Received by editor(s) in revised form: May 5, 2013
Published electronically: October 3, 2014
Additional Notes: The first author was partially supported by the MICINN grant numbers MTM2008-01486 and MTM2011-26995-C02-01.
Communicated by: Nimish Shah
Article copyright: © Copyright 2014 American Mathematical Society