Weak dissipation drives and enhances Wada basins in three-dimensional chaotic scattering

TL;DR

This paper demonstrates that weak dissipation in three-dimensional chaotic scattering systems can induce and enhance Wada basin boundaries, which are absent without dissipation, revealing a novel topological effect.

Contribution

It shows that weak dissipation transforms non-Wada basins into Wada basins in 3D Hamiltonian systems, a phenomenon not present in 2D systems.

Findings

Weak dissipation induces Wada basins in 3D systems.

Wada points emerge on basin boundaries under weak dissipation.

Wada basins are structurally stable with weak dissipation.

Abstract

Chaotic scattering in three dimensions has not received as much attention as in two dimensions so far. In this paper, we deal with a three-dimensional open Hamiltonian system whose Wada basin boundaries become non Wada when the critical energy value is surpassed in the absence of dissipation. In particular, we study here the dissipation effects on this topological change, which has no analogy in two dimensions. Hence, we find that non-Wada basins, expected in the absence of dissipation, transform themselves into partially Wada basins when a weak dissipation reduces the system energy below the critical energy. We provide numerical evidence of the emergence of the Wada points on the basin boundaries under weak dissipation. According to the paper findings, Wada basins are typically driven, enhanced and, consequently, structurally stable under weak dissipation in three-dimensional open Hamiltonian systems.