Homoclinic tangencies, generating partitions and curvature of invariant manifolds

Year: 1991

Authors: Giovannini F., Politi A.

Autors Affiliation: Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy

Abstract: A method to compute the curvature of the unstable manifold is introduced and applied to Henon map and Duffing attractor, showing that it allows us to locate the homoclinic tangencies and, in turn, to construct a generating partition. The probability distribution of curvature-values is investigated, showing a power-law decay. Finally, the shape of the multifractal spectrum of effective Liapunov exponents in non-hyperbolic systems is discussed.

Journal/Review: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL

Volume: 24 (8)      Pages from: 1837  to: 1887

KeyWords: Attractors
DOI: 10.1088/0305-4470/24/8/024

Citations: 22
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