5,186 research outputs found
Stickiness in mushroom billiards
We investigate dynamical properties of chaotic trajectories in mushroom
billiards. These billiards present a well-defined simple border between a
single regular region and a single chaotic component. We find that the
stickiness of chaotic trajectories near the border of the regular region occurs
through an infinite number of marginally unstable periodic orbits. These orbits
have zero measure, thus not affecting the ergodicity of the chaotic region.
Notwithstanding, they govern the main dynamical properties of the system. In
particular, we show that the marginally unstable periodic orbits explain the
periodicity and the power-law behavior with exponent observed in the
distribution of recurrence times.Comment: 7 pages, 6 figures (corrected version with a new figure
Structure of resonance eigenfunctions for chaotic systems with partial escape
Physical systems are often neither completely closed nor completely open, but instead are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main properties of resonance eigenfunctions of chaotic quantum systems with partial escape. We construct a family of conditionally invariant measures with varying decay rates by interpolating between the natural measures of the forward and backward dynamics. Numerical simulations in a representative system show that our classical measures correctly describe the main features of the quantum eigenfunctions: their multifractal phase-space distribution, their product structure along stable and unstable directions, and their dependence on the decay rate. The (Jensen-Shannon) distance between classical and quantum measures goes to zero in the semiclassical limit for long- and short-lived eigenfunctions, while it remains finite for intermediate cases
Nontwist non-Hamiltonian systems
We show that the nontwist phenomena previously observed in Hamiltonian
systems exist also in time-reversible non-Hamiltonian systems. In particular,
we study the two standard collision/reconnection scenarios and we compute the
parameter space breakup diagram of the shearless torus. Besides the Hamiltonian
routes, the breakup may occur due to the onset of attractors. We study these
phenomena in coupled phase oscillators and in non-area-preserving maps.Comment: 7 pages, 5 figure
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