Non-autonomous Hénon-Heiles systems

Non-autonomous Hénon-Heiles Systems

Scaling similarity solutions of three integrable PDEs, namely the Sawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered. It is shown that the resulting ODEs may be written as non-autonomous Hamiltonian equations, which are time-dependent generalizations of the well-known integrable Hénon-Heiles systems. The (time-dependent) Hamiltonians are given by logarithmic derivativ...

Statistical mechanics of Hénon-Heiles oscillators.

Statistical mechanics is an asymptotic theory valid in the limit of an infinite number of degrees of freedom. The study of small-dimensional chaos, starting from the papers by Lorenz [1]and Henon and Heiles [2], raises the question: What is essential for the laws of statistical mechanics to be true —a large number of degrees of freedom or chaos? For ergodic Hamiltonian systems the answer was gi...

Possible conserved quantity for the Hénon-Heiles problem.

2 00 6 Painlevé Property of the Hénon - Heiles Hamiltonians

— Time independent Hamiltonians of the physical type H = (P 2 1 + P 2 2 )/2 + V (Q1, Q2) pass the Painlevé test for only seven potentials V , known as the Hénon-Heiles Hamiltonians, each depending on a finite number of free constants. Proving the Painlevé property was not yet achieved for generic values of the free constants. We integrate each missing case by building a birational transformatio...

Chaos around a Hénon-Heiles-inspired exact perturbation of a black hole.

A solution of the Einstein’s equations that represents the superposition of a Schwarszchild black hole with both quadrupolar and octopolar terms describing a halo is exhibited. We show that this solution, in the Newtonian limit, is an analog to the well known Hénon-Heiles potential. The integrability of orbits of test particles moving around a black hole representing the galactic center is stud...