منابع مشابه
Chaotic attractors of relaxation oscillators
We develop a general technique for proving the existence of chaotic attractors for three-dimensional vector fields with two time scales. Our results connect two important areas of dynamical systems: the theory of chaotic attractors for discrete two-dimensional Henon-like maps and geometric singular perturbation theory. Two-dimensional Henon-like maps are diffeomorphisms that limit on non-invert...
متن کاملPhase Mixing of Chaotic Orbits as an Irreversible “relaxation” Mechanism*
Orbits that are chaotic will tend to phase-mix exponentially through their accessible phase space. This phenomenon, commonly called “chaotic mixing”, stands in marked contrast to phase mixing of regular orbits. It is inherently irreversible, and thus its associated e-folding time scale sets a condition on any process envisioned for emittance compensation. Accordingly, two questions arise. First...
متن کاملExponential Divergence and Long Time Relaxation in Chaotic Quantum Dynamics.
Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum–classical correspondence in a K-system: as h̄ → 0, the classical chaotic behavior is shown to emerge smoothly and exactly. The quantum dynamics near the classical limit displays both exponential separation of adjacent distributions and long time relaxation, two characteristic features of ...
متن کاملFluctuations in the relaxation dynamics of mixed chaotic systems.
The relaxation dynamics in mixed chaotic systems are believed to decay algebraically with a universal decay exponent that emerges from the hierarchical structure of the phase space. Numerical studies, however, yield a variety of values for this exponent. In order to reconcile these results, we consider an ensemble of mixed chaotic systems approximated by rate equations and analyze the fluctuati...
متن کاملEffect of noise on the relaxation to an invariant probability measure of nonhyperbolic chaotic attractors.
We study the influence of external noise on the relaxation to an invariant probability measure for two types of nonhyperbolic chaotic attractors, a spiral (or coherent) and a noncoherent one. We find that for the coherent attractor the rate of mixing changes under the influence of noise, although the largest Lyapunov exponent remains almost unchanged. A mechanism of the noise influence on mixin...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1969
ISSN: 0024-3795
DOI: 10.1016/0024-3795(69)90028-7