Numerical Studies of Hamiltonian Systems and Application to Galactic Potentials

TL;DR

This paper reviews the seminal 1964 work on numerical experiments in galactic dynamics, emphasizing the importance of the third integral of motion in Hamiltonian systems and its applications to galactic potentials.

Contribution

It provides a commentary on Henon and Heiles's foundational paper, highlighting its significance and encouraging further study in dynamical systems and galactic dynamics.

Findings

Numerical experiments support the existence of a third integral of motion.

The paper underscores the relevance of Hamiltonian systems in galactic dynamics.

It promotes the study of nonlinear dynamical phenomena in astrophysics.

Abstract

The talk consisted mainly in commenting in a linear way the seminal paper in 1964 by Michel Henon and graduate student Carl Heiles at Princeton University: "The applicability of the third integral of motion: Some numerical experiments" in the field of galactic dynamics. Instead of repeating here the lecture of the paper, we advise the reader interested in dynamical systems to study this "must" reading.