Periodic Dynamics of a Class of Non-autonomous Contact Hamiltonian Systems

In this paper, we investigate the existence, number and stability of periodic orbits for the following contact Hamiltonian system H(p,q,s,t)=p22m+G(t,q,m)-mdq+cs(c>0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H(p,q,s,t)=\frac{p^{2}}{2m}+G(t,q,m)-mdq+cs(c>0)$$\end{document}. At the same time, unbounded conditions of each solution are also given. The contact Hamiltonian system actually represents a kind of physical phenomenon with non-conservation of energy, but the contact Hamiltonian system studied in this paper represents a one-dimensional damped oscillator system with constant variable sign damping coefficient under certain conditions. Therefore, it is of great physical significance to study the periodic dynamic properties of such system.