Measuring the total amount of chaos in some Hamiltonian Systems
Carles Sim\'o
Departament de Matem\`atica Aplicada i An\`alisi, Universitat de Barcelona
Gran Via 585, 08007 Barcelona, Catalunya
carles@maia.ub.es

Abstract

We consider some simple Hamiltonian systems, variants or generalizations of the
H\'enon-Heiles system, in two and three degrees of freedom, around a positive
definite elliptic point, in resonant and non-resonant cases. After reviewing
some theoretical background, we determine a measure of the domain of chaoticity
by looking at the frequency of positive Lyapunov exponents in a sample of
initial conditions. The question we study is how this measure depends on the
energy and parameters and which are the dynamical objects responsible for the
observed behaviour.