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One-parameter families of smooth interval maps: Density of hyperbolicity and robust chaos


Author: Sebastian van Strien
Journal: Proc. Amer. Math. Soc. 138 (2010), 4443-4446
MSC (2010): Primary 37E05, 37Gxx, 37Dxx
DOI: https://doi.org/10.1090/S0002-9939-2010-10446-X
Published electronically: June 22, 2010
MathSciNet review: 2680068
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Abstract: In this paper we will discuss the notion of robust chaos and show that (i) there are natural one-parameter families of interval maps with robust chaos and (ii) hyperbolicity is dense within generic one-parameter families (and so these families are not robustly chaotic).


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Additional Information

Sebastian van Strien
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: strien@maths.warwick.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2010-10446-X
Received by editor(s): December 3, 2009
Received by editor(s) in revised form: February 15, 2010
Published electronically: June 22, 2010
Communicated by: Yingfei Yi
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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