Orbital dynamics on invariant sets of contact Hamiltonian systems

Abstract

<p style='text-indent:20px;'>In this paper, we shall give new insights on dynamics of contact Hamiltonian flows, which are gaining importance in several branches of physics as they model a dissipative behaviour. We divide the contact phase space into three parts, which are corresponding to three differential invariant sets <inline-formula><tex-math id="M1">\begin{document}$ \Omega_\pm, \Omega_0 $\end{document}</tex-math></inline-formula>. On the invariant sets <inline-formula><tex-math id="M2">\begin{document}$ \Omega_\pm $\end{document}</tex-math></inline-formula>, under some geometric conditions, the contact Hamiltonian system is equivalent to a Hamiltonian system via the Hölder transformation. The invariant set <inline-formula><tex-math id="M3">\begin{document}$ \Omega_0 $\end{document}</tex-math></inline-formula> may be composed of several equilibrium points and heteroclinic orbits connecting them, on which contact Hamiltonian system is conservative. Moreover, we have shown that, under general conditions, the zero energy level domain is a domain of attraction. In some cases, such a domain of attraction does not have nontrivial periodic orbits. Some interesting examples are presented.</p>