Transi\c{c}\~ao de fase no sistema de H\'enon-Heiles (Phase transition in the Henon-Heiles system)

TL;DR

This paper investigates the phase transition and dynamical behavior of the Henon-Heiles system, highlighting how chaos expands with energy and identifying phenomena like stability islands and stickiness.

Contribution

It introduces a formalism for analyzing the Henon-Heiles system and provides a qualitative approach to understanding its phase space dynamics and chaos development.

Findings

Chaotic regions grow with increasing energy

Stable islands persist around stable points

Sticky phenomena are observed in phase space

Abstract

The Henon-Heiles system was originally proposed to describe the dynamical behavior of galaxies, but this system has been widely applied in dynamical systems by exhibit great details in phase space. This work presents the formalism to describe Henon-Heiles system and a qualitative approach of dynamics behavior. The growth of chaotic region in phase space is observed by Poincare Surface of Section when the total energy increases. Island of regularity remain around stable points and relevants phenomena appear, such as sticky.