2019
DOI: 10.48550/arxiv.1903.08591
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A spectral decomposition of the attractor of piecewise contracting maps of the interval

A. Calderón,
E. Catsigeras,
P. Guiraud

Abstract: We study the asymptotic dynamics of piecewise contracting maps defined on a compact interval. For maps that are not necessarily injective, but have a finite number of local extrema and discontinuity points, we prove the existence of a decomposition of the support of the asymptotic dynamics into a finite number of minimal components. Each component is either a periodic orbit or a minimal Cantor set and such that the ω-limit set of (almost) every point in the interval is exactly one of these components. Moreover… Show more

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