Fractal Dimension of Higher-Dimensional Chaotic Repellors

Abstract

Using examples we test formulae previously conjectured to give the fractal information dimension of chaotic repellors and their stable and unstable manifolds in ``typical'' dynamical systems in terms of the Lyapunov exponents and the characteristic escape time from the repellor. Our main example, a three-dimensional chaotic scattering billiard, yields a new structure for its invariant manifolds. This system also provides an example of a system which is not typical and illustrates how perturbation to the system restores typicality and the applicability of the dimension formulae.

arXiv comment38 pages, 8 figures, to be published in Physica D

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