Universality in the chaotic dynamics associated with saddle-centers critical points

H.P. de Oliveira, I.Damião Soares and E.V. Tonini

Physica A: Statistical Mechanics and its Applications, 2001, vol. 295, issue 3, 348-358

Abstract: We describe a new statistical pattern characteristic of saddle-center critical points in the dynamics of non-integrable Hamiltonian systems, associated with the partition of the Hamiltonian into rotational motion energy and hyperbolic motion energy pieces in a linear neighborhood of the saddle-center. The distribution of hyperbolic energy of orbits visiting a neighborhood of the saddle-center defines a statistical law that, for a large range of values of the hyperbolic energy, has the form p(z)∼z−γ, in a regime of high nonintegrability. We present numerical evidence to support the conjecture that this pattern is universal for any Hamiltonian system with one or several saddle-centers. The parameter γ appears as a universal characteristic associated with the chaotic dynamics of saddle-centers.

Keywords: Chaos and universality; Saddle-centers; Hénon–Heiles Hamiltonian; Non-extensive statistical mechanics (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:295:y:2001:i:3:p:348-358

DOI: 10.1016/S0378-4371(01)00122-4

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