Effective dynamics in Hamiltonian systems with mixed phase space
arXiv:nlin/0503060 · doi:10.1103/PhysRevE.71.036215
Abstract
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.
4 figures, Revtex
References in corpus (7)
- The Limited Scaling Range of Empirical Fractals
- Long-Time Correlations in the Stochastic Regime
- Fractal Conductance Fluctuations in Generic Chaotic Cavities
- Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients
- Simple Maps with Fractal Diffusion Coefficients
- Mixmaster chaos
- Reactive dynamics of inertial particles in nonhyperbolic chaotic flows
Cited by in corpus (11)
- A Poissonian explanation for heavy-tails in e-mail communication
- Frontiers of chaotic advection
- Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space
- Stickiness in mushroom billiards
- Open-flow mixing: Experimental evidence for strange eigenmodes
- Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems
- Quantum signatures of classical multifractal measures
- Emerging attractors and the transition from dissipative to conservative dynamics
- Slim Fractals: The Geometry of Doubly Transient Chaos
- Power-law trapping in the volume-preserving Arnold-Beltrami-Childress map
- Fractals in rate-induced tipping