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

Author

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

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.

Suggested Citation

  • de Oliveira, H.P. & Soares, I.Damião & Tonini, E.V., 2001. "Universality in the chaotic dynamics associated with saddle-centers critical points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 348-358.
    • Handle: RePEc:eee:phsmap:v:295:y:2001:i:3:p:348-358
    DOI: 10.1016/S0378-4371(01)00122-4
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    Cited by:

    1. Bafghi, Seyed Mohammad Amin Tabatabaei & Kamalvand, Mohammad & Morsali, Ali & Bozorgmehr, Mohammad Reza, 2018. "Radial distribution function within the framework of the Tsallis statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 857-867.

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