Effective dynamics in Hamiltonian systems with mixed phase space

Details Effective dynamics in Hamiltonian systems with mixed phase space Effective dynamics in Hamiltonian systems with mixed phase space

2005-03-29

arxiv.org/abs/nlin/0503060v1

Phys. Rev. E 71, 036215 (2005)

Nonlinear Sciences

Chaotic Dynamics

4 figures, Revtex

Scientific paper

10.1103/PhysRevE.71.036215

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.

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