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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Skew product attractors and concavity
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by Lluís Alsedà and Michał Misiurewicz PDF
Proc. Amer. Math. Soc. 143 (2015), 703-716 Request permission

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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Additional Information
  • Lluís Alsedà
  • Affiliation: Departament de Matemàtiques, Edifici Cc, Universitat Autònoma de Barcelona, 08913 Cerdanyola del Vallès, Barcelona, Spain
  • MR Author ID: 212847
  • Email: alseda@mat.uab.cat
  • Michał Misiurewicz
  • Affiliation: Department of Mathematical Sciences, Indiana University–Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, Indiana 46202
  • MR Author ID: 125475
  • Email: mmisiure@math.iupui.edu
  • 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
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 703-716
  • MSC (2010): Primary 37C55, 37C70
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12271-4
  • MathSciNet review: 3283657