Fractal attractors induced by β-shifts

Jörg Neunhäuserer

Chaos, Solitons & Fractals, 2019, vol. 123, issue C, 87-90

Abstract: We describe a class of fractal attractors induced by β-shifts. We use a coding by these shifts to show that the systems are mixing with topological entropy log β and have an ergodic measure of full entropy. This demonstrates that, symbolic dynamics can be used to determine significant properties of a geometric model in chaotic dynamics. Moreover we determine the Hausdorff dimension of the attractor induced by β-shifts. Since the dimension is in (1,2) these attractors are fractals, we have thus found a new class of fractal attractors in the theory of dynamical systems.

Keywords: β-shift; Attractor; Symbolic dynamics; Fractals; Dimension; Entropy (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:123:y:2019:i:c:p:87-90

DOI: 10.1016/j.chaos.2019.03.025

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