Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems

Details Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems

2011-11-30

arxiv.org/abs/1111.7135v2

Nonlinear Sciences

Chaotic Dynamics

To appear in "Chaos" special issue: "Statistical Mechanics and Billiard-Type Dynamical Systems"; 6 pages, 10 figures

Scientific paper

The dynamics in weakly chaotic Hamiltonian systems strongly depends on initial conditions and little can be affirmed about generic behaviors. Using two distinct Hamiltonian systems, namely one particle in an open rectangular billiard and four particles globally coupled on a discrete lattice, we show that in these models the transition from integrable motion to weak chaos emerges via chaotic stripes as the nonlinear parameter is increased. The stripes represent intervals of initial conditions which generate chaotic trajectories and increase with the nonlinear parameter of the system. In the billiard case the initial conditions are the injection angles. For higher-dimensional systems and small nonlinearities the chaotic stripes are the initial condition inside which Arnold diffusion occurs.

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