For conservative dynamical systems, the invariant sets which are in a sense the analog of the strange attractors of dissipative systems, namely the closures of homoclinic orbits of hyperbolic points, are known to have in general integral dimensions. We show however, working numerically on a particular model, that actual numerical estimates for perturbations of an integrable system will necessarily exhibit an apparent fractal dimension, which will be the effective one to all practical purpose. A simple scheme of interpretation is also given.

Apparent fractal dimensions in conservative dynamical systems / G. Benettin, D. Casati, L. Galgani, A. Giorgilli, L. Sironi. - In: PHYSICS LETTERS A. - ISSN 0375-9601. - 118:7(1986), pp. 325-330.

Apparent fractal dimensions in conservative dynamical systems

L. Galgani;A. Giorgilli;
1986

Abstract

For conservative dynamical systems, the invariant sets which are in a sense the analog of the strange attractors of dissipative systems, namely the closures of homoclinic orbits of hyperbolic points, are known to have in general integral dimensions. We show however, working numerically on a particular model, that actual numerical estimates for perturbations of an integrable system will necessarily exhibit an apparent fractal dimension, which will be the effective one to all practical purpose. A simple scheme of interpretation is also given.
Settore MAT/07 - Fisica Matematica
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/243950
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