One-Parameter Families of Smooth Interval Maps: Density of Hyperbolicity and Robust Chaos

2009/12/03 by Sebastian van Strien, van Strien, Sebastian
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #Mathematical Dynamics and Fractals #math.DS #msc:37Dxx #msc:37E05 #msc:37Gxx

paper · pdf · doi:10.48550/arxiv.0912.0656

arxiv created 2009/12/03 · arxiv updated 2009/12/08

Abstract

In this note we will discuss the notion of robust chaos, and show that (i) there are natural one-parameter families 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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