Basin entropy and the impact of the escape positioning in an open area-preserving map

TL;DR

This paper investigates how the placement of exits influences the complexity of escape basins in an open area-preserving map, using basin entropy to quantify the effects in a tokamak particle transport model.

Contribution

It introduces a systematic analysis of how exit positioning affects basin entropy and escape basin complexity in open Hamiltonian systems.

Findings

Exit placement significantly alters basin entropy.

Abrupt changes in basin entropy occur with different exit configurations.

Escape basin complexity is highly sensitive to exit positioning.

Abstract

The main properties of a dynamical system can be analyzed by examining the corresponding basins, either attraction basins in dissipative systems or escape basins in open Hamiltonian systems and area-preserving maps. In the latter case, the selection of the openings is crucial, as the way exits are chosen can directly influence the results. This study explores the impact of different opening choices on the escape basins by employing a model of particles transported along field lines in tokamaks with reversed shear. We quantitatively evaluate these phenomena using the concept of basin entropy across various system configurations. Our findings reveal that the positioning of the exits significantly affects the complexity and behavior of the escape basins, with remarkable abrupt changes in basin entropy linked to the choice of exits.