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

• DOI: 10.1007/s44198-022-00098-x
• Publication Date: 2022-12-26T05:02:55Z
• Authors: Zhanyong Li; Yaozong Tang; A. Mina Sha Bier; Jianguo Ye
• Keywords: 0101 mathematics; 01 natural sciences

Abstract In this paper, we investigate the existence, number and stability of periodic orbits for following contact Hamiltonian system $$H(p,q,s,t)=\frac{p^{2}}{2m}+G(t,q,m)-mdq+cs(c&gt;0)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> <mml:mi>s</mml:mi> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mfrac> <mml:msup> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>m</mml:mi> </mml:mfrac> <mml:mo>+</mml:mo> <mml:mi>G</mml:mi> <mml:mo>-</mml:mo> <mml:mi>d</mml:mi> <mml:mi>c</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:math> . At same time, unbounded conditions each solution are also given. The actually represents a kind physical phenomenon with non-conservation energy, but studied in paper one-dimensional damped oscillator constant variable sign damping coefficient under certain conditions. Therefore, it is great significance to study dynamic properties such system.