Effective dynamics in Hamiltonian systems with mixed phase space

Adilson E. Motter*, Alessandro P S De Moura, Celso Grebogi, Holger Kantz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


An adequate characterization of the dynamics of Hamiltonian systems at physically relevant scales has been largely lacking. Here we investigate this fundamental problem and we show that the finite-scale Hamiltonian dynamics is governed by effective dynamical invariants, which are significantly different from the dynamical invariants that describe the asymptotic Hamiltonian dynamics. The effective invariants depend both on the scale of resolution and the region of the phase space under consideration, and they are naturally interpreted within a framework in which the nonhyperbolic dynamics of the Hamiltonian system is modeled as a chain of hyperbolic systems.

Original languageEnglish (US)
Article number036215
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number3
StatePublished - Mar 2005

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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