Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems

Abstract

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.

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

References in corpus (7)

• Graphene quantum dots: Beyond a Dirac billiard
• Stickiness in mushroom billiards
• Instability statistics and mixing rates
• Soft wall effects on interacting particles in billiards
• Origin of chaos in soft interactions and signatures of nonergodicity
• Gauss map and Lyapunov exponents of interacting particles in a billiard
• Three unequal masses on a ring and soft triangular billiards

Cited by in corpus (3)

• Conservative Generalized Bifurcation Diagrams
• Characterizing weak chaos in nonintegrable Hamiltonian systems: the fundamental role of stickiness and initial conditions
• Chaos and Regularity in an Anisotropic Soft Squircle Billiard