Resonant behavior and unpredictability in forced chaotic scattering

TL;DR

This paper investigates how weak periodic forcing influences the fractal structure and unpredictability of escape dynamics in chaotic scattering systems, revealing resonant behaviors and the destruction of stable regions.

Contribution

It introduces the analysis of fractal dimension and basin entropy in forced chaotic scattering, highlighting resonant effects and the destruction of KAM islands near the main resonance frequency.

Findings

Fractal dimension decreases near the resonance frequency.

Basin entropy reduces due to shrinking KAM islands.

Decay rate minimum indicates complete destruction of KAM islands.

Abstract

Chaotic scattering in open Hamiltonian systems is a topic of fundamental interest in physics, which has been mainly studied in the purely conservative case. However, the effect of weak perturbations in this kind of systems has been an important focus of interest in the last decade. In a previous work, the authors studied the effects of a periodic forcing in the decay law of the survival probability, and they characterized the global properties of escape dynamics. In the present paper, we add two important issues in the effects of periodic forcing: the fractal dimension of the set of singularities in the scattering function, and the unpredictability of the exit basins, which is estimated by using the concept of basin entropy. Both the fractal dimension and the basin entropy exhibit a resonant-like decrease as the forcing frequency increases. We provide a theoretical reasoning, which could justify this decreasing in the fractality near the main resonant frequency, that appears for $\omega \approx 1$. We attribute the decrease in the basin entropy to the reduction of the area occupied by the KAM islands and the basin boundaries when the frequency is close to the resonance. Finally, the decay rate of the exponential decay law shows a minimum value of the amplitude, $A_c$, which reflects the complete destruction of the KAM islands in the resonance. We expect that this work could be potentially useful in research fields related to chaotic Hamiltonian pumps, oscillations in chemical reactions and companion galaxies, among others.