Probabilistic description of dissipative chaotic scattering

Abstract

We investigate the extent to which the probabilistic properties of a chaotic scattering system with dissipation can be understood from the properties of the dissipation-free system. For large energies $E$, a fully chaotic scattering leads to an exponential decay of the survival probability $P(t)\sim e^{-\kappa t}$ with an escape rate $\kappa$ that decreases with $E$. Dissipation $\gamma >0$ leads to the appearance of different finite-time regimes in $P(t)$. We show how these different regimes can be understood for small $\gamma \ll 1$ and $t\gg 1/{\kappa }_0$ from the effective escape rate ${\kappa }_{\gamma }(t)={\kappa }_0(E(t))$ (including the non-hyperbolic regime) until the energy reaches a critical value $E_c$ at which no escape is possible. More generally, we argue that for small dissipation $\gamma$ and long times $t$ the surviving trajectories in the dissipative system are distributed according to the conditionally invariant measure of the conservative system at the corresponding energy $E(t)<E(0)$. Quantitative predictions of our general theory are compared with numerical simulations in the Henon-Heiles model.

arXiv comment11 pages, 5 figures; For associated repository with codes, see https://github.com/LnBn/DissipativeScattering

References in corpus (9)

• Leaking Chaotic Systems
• Dissipative chaotic scattering
• Poincare recurrences and transient chaos in systems with leaks
• Doubly Transient Chaos: The Generic Form of Chaos in Autonomous Dissipative Systems
• Reactive dynamics of inertial particles in nonhyperbolic chaotic flows
• Chaotic Systems with Absorption
• Stochastic perturbations in open chaotic systems: random versus noisy maps
• An overview of the escape dynamics in the Henon-Heiles Hamiltonian system
• Slim Fractals: The Geometry of Doubly Transient Chaos

Cited by in corpus (1)

• Chaotic resetting: A resetting strategy for deterministic chaotic systems