On the Hausdorff Dimension of Piecewise Hyperbolic Attractors
Tomas Persson
TL;DR
This paper investigates the Hausdorff dimension of attractors in non-invertible piecewise hyperbolic maps, establishing a formula based on Lyapunov exponents under certain conditions, with explicit examples provided.
Contribution
It introduces a formula for the Hausdorff dimension of attractors in piecewise hyperbolic maps using Lyapunov exponents, under a transversality condition, with concrete examples.
Findings
Dimension formula in terms of Lyapunov exponents
Explicit examples satisfying the transversality condition
Application to non-invertible piecewise hyperbolic maps
Abstract
We study non-invertible piecewise hyperbolic maps in the plane. The Hausdorff dimension of the attractor is calculated in terms of the Lyapunov exponents, provided that the map satisfies a transversality condition. Explicit examples of maps for which this condition holds are given.
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Taxonomy
TopicsMathematical Dynamics and Fractals · advanced mathematical theories · Quantum chaos and dynamical systems