Basin topology in dissipative chaotic scattering

Area of Science:

• * Physics
• * Nonlinear Dynamics
• * Fluid Mechanics

Background:

• * Chaotic scattering in open Hamiltonian systems is fundamental to particle transport.
• * Nonhyperbolic chaotic scattering is structurally unstable under weak dissipation, leading to exponential decay.
• * Previous studies focused on discrete maps, leaving continuous systems less explored.

Purpose of the Study:

• * Extend the understanding of chaotic scattering to continuous-time Hamiltonian systems.
• * Investigate the impact of weak dissipation on the basin structure of scattering dynamics.
• * Determine the stability of complex basin topologies under dissipation.

Main Methods:

• * Utilized the Henon-Heiles system as a prototype continuous-time Hamiltonian model.
• * Employed numerical simulations to analyze scattering trajectories and basin structures.
• * Developed a geometric theory to explain observed phenomena.

Main Results:

• * Confirmed that weak dissipation destabilizes nonhyperbolic chaotic scattering characteristics.
• * Discovered that Wada basin boundaries are common and structurally stable under weak dissipation.
• * Demonstrated stability of complex basin topology despite changes in other scattering dynamics.

Conclusions:

• * Weak dissipation has a stabilizing effect on Wada basin boundaries in chaotic scattering.
• * The complex basin topology, characterized by Wada boundaries, exhibits robustness against dissipation.
• * Findings are significant for modeling advection and transport of inertial particles in fluid flows.