| Popis: |
We study the dynamics of a one parameter family of two degrees of freedom Hamiltonian systems that includes the Henon-Heiles system. We show that several dynamical properties of this family, like the existence of large stochastic regions in certain parts of the phase space, are related to two canonical invariants that can be explicitly computed. These two invariants characterize universality classes of two degrees of freedom Hamiltonian systems with orbits homoclinic (bi-asymptotic) to saddle-center equilibria (related to pairs of real and pure imaginary eigenvalues). Examples of systems that can be described by Hamiltonians in this universality class are the planar three-body system, charged particles in a magnetic dipole field (Stormer problem), buckled beams, some stationary plasma systems. |
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