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Orbital dynamics on invariant sets of contact Hamiltonian systems. (English) Zbl 1510.37100

The paper is focused on the dynamics of contact Hamiltonian flows. The authors divide the contact phase space into three parts, corresponding to three differential invariant sets, \(\Omega_{\pm}\), \(\Omega_{0}\). In the invariant sets \(\Omega_{\pm}\), under some geometric conditions, the contact Hamiltonian system is equivalent to a Hamiltonian system via Hölder transformations. Under certain conditions, the invariant set \(\Omega_{0}\) may be a \(2n\)-dimensional closed submanifold consisting of several equilibrium points and heteroclinic orbits. It is shown that, under general conditions the set \(\Omega_{0}\) is a zero-energy level domain if and only if it is a domain of attraction. In some cases, such a domain of attraction does not have nontrivial periodic orbits.

MSC:

37J55 Contact systems
37J46 Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems
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