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Measuring the total amount of chaos in some Hamiltonian systems

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  • We consider some simple Hamiltonian systems, variants or generalizations of the Hénon-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.
    Mathematics Subject Classification: Primary: 70H07, 70K70; Secondary: 34D08, 37J40, 37J45, 37M25.


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