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Periodic orbits of a dynamical system in a compound central field and a perturbed billiards system. (English) Zbl 0810.58014

The paper treats the Hamiltonian flow corresponding to a compound central field in the Euclidean plane which is determined by finitely many bell- shaped potential functions with finite range. It is shown that, if the total energy is sufficiently small, the symbolic representation of the Hamiltonian flow can be constructed in terms of perturbed billiards systems. This is applied to study the distribution of the periodic solutions of the involved Hamilton equation.
Reviewer: D.Motreanu (Iaşi)

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37G99 Local and nonlocal bifurcation theory for dynamical systems
37C10 Dynamics induced by flows and semiflows
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