2005/03/18 by Adilson E. Motter, Alessandro P. S. de Moura, Celso Grebogi +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Theoretical and Computational Physics #cond-mat.stat-mech #math.DS #nlin.CD
paper · pdf · doi:10.1103/physreve.71.036215
published as Phys. Rev. E 71, 036215 (2005) · 4 figures, Revtex
openalex publication_date 2005/03/18 · arxiv created 2005/03/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.