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

van Strien, Sebastian

doi:10.1090/S0002-9939-2010-10446-X

One-parameter families of smooth interval maps: Density of hyperbolicity and robust chaos
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by Sebastian van Strien

Proc. Amer. Math. Soc. 138 (2010), 4443-4446

DOI: https://doi.org/10.1090/S0002-9939-2010-10446-X

Published electronically: June 22, 2010

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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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