A New Discrete Hénon-Heiles System

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...

Lyapunov stability for a generalized Hénon-Heiles system in a rotating reference frame

In this paper we focus on a generalized Hénon–Heiles system in a rotating reference frame, in such a way that Lagrangian-like equilibrium points appear. Our goal is to study their nonlinear stability properties to better understand the dynamics around these points. We show the conditions on the free parameters to have stability and we prove the superstable character of the origin for the classi...

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...

Periodic orbit theory for the Hénon-Heiles system in the continuum region.

We investigate the resonance spectrum of the Hénon-Heiles potential up to twice the barrier energy. The quantum spectrum is obtained by the method of complex coordinate rotation. We use periodic orbit theory to approximate the oscillating part of the resonance spectrum semiclassically and Strutinsky smoothing to obtain its smooth part. Although the system in this energy range is almost chaotic,...