# Escaping from a degenerate version of the four hill potential

## TL;DR

This study analyzes how energy levels affect escape dynamics in the four hill potential, revealing the influence on escape times, channels, and basin fractality through grid classification and basin diagrams.

## Contribution

It introduces a detailed analysis of energy-dependent escape mechanisms and fractal basin structures in the four hill potential using grid classification methods.

## Key findings

- Energy significantly affects escape channels and times.
- Higher energy reduces basin fractality and entropy.
- Escape dynamics vary with initial conditions and energy levels.

## Abstract

We examine the escape from the four hill potential by using the method of grid classification, when polar coordinates are used for expressing the initial conditions of the orbits. In particular, we investigate how the energy of the orbits influences several aspects of the escape dynamics, such as the escape period and the chosen channels of escape. Color-coded basin diagrams are deployed for presenting the basins of escape using multiple types of planes with two dimensions. We demonstrate that the value of the energy highly influences the escape mechanism of the orbits, as well as the degree of fractality of the dynamical system, which is numerically estimated by computing both the fractal dimension and the entropy of the basin boundaries.