Recurrence and Stickiness in the Noisy Harper Map

Abstract

When three types of noise are introduced to the area-preserving Harper map, the Poincaré recurrence statistic (PRS) exhibits an extended tail, corresponding to an increased probability of longer recurrence times. For a deterministic case with a mixture of regular and chaotic orbits, regular islands are responsible for a power-law decay in the recurrence distribution. Noise perturbations allow trajectories to access the interior of the islands, and this can enhance their trapping effect, causing many orbits to take longer to return to a neighborhood of their initial conditions and resulting in a slower power-law decay on an intermediate time scale. On a longer time scale, however, the noisy PRS exhibits exponential decay, eventually falling below the deterministic PRS. We compare distributions of trapping and visit times to islands with recurrence times to show the importance of noise in creating tails in the PRS. A simple model of the dynamics -- a Markov chain with three states -- demonstrates how the slower decay can be caused by noise allowing entry to a previously inaccessible island.

References in corpus (21)

• Long-Time Correlations in the Stochastic Regime
• Stochastic Ion Heating by a Lower Hybrid Wave: II
• Thirty Years of Turnstiles and Transport
• Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space
• Asymptotic Statistics of Poincaré Recurrences in Hamiltonian Systems with Divided Phase Space
• On universality of algebraic decays in Hamiltonian systems
• Average exit times in volume preserving maps
• Effect of Noise on the Standard Mapping
• Poincare recurrences and transient chaos in systems with leaks
• Noise-enhanced trapping in chaotic scattering
• Escape Rates and Physically Relevant Measures for Billiards with Small Holes
• What is the mechanism of power-law distributed Poincaré recurrences in higher-dimensional systems?
• Stickiness and recurrence plots: an entropy-based approach
• Random fluctuation leads to forbidden escape of particles
• Stickiness in generic low-dimensional Hamiltonian systems: A recurrence-time statistics approach
• Universal Exponent for Transport in Mixed Hamiltonian Dynamics
• Exploring conservative islands using correlated and uncorrelated noise
• Noise activates escapes in closed Hamiltonian systems
• Transport in Hamiltonian systems with slowly changing phase space structure
• Designing a Finite-Time Mixer: Optimizing Stirring for Two-Dimensional Maps
• Escape-rate response to noise of all amplitudes in leaky chaos