Minimal P-cyclic periodic brake orbits in Hamiltonian systems
نویسندگان
چکیده
<p style='text-indent:20px;'>We study the Maslov-type index theory under a special Lagrangian boundary condition, namely <inline-formula><tex-math id="M2">\begin{document}$ (P,L_0) $\end{document}</tex-math></inline-formula> which comes naturally in of brake orbits id="M3">\begin{document}$ P $\end{document}</tex-math></inline-formula>-invariant Hamiltonian systems with certain orthogonal symplectic matrix id="M4">\begin{document}$ satisfying id="M5">\begin{document}$ P^p = {\rm Id} $\end{document}</tex-math></inline-formula>. In this paper, we give some new iteration inequalities condition. As applications, consider minimal cyclic period problems for first order nonlinear autonomous reversible id="M6">\begin{document}$ $\end{document}</tex-math></inline-formula>-symmetric systems. We prove that if id="M7">\begin{document}$ R(\theta_1)\diamond\ldots\diamond R(\theta_n) and id="M8">\begin{document}$ \theta_i\in [0,\pi] each id="M9">\begin{document}$ 1\leq i\leq n $\end{document}</tex-math></inline-formula>, is strictly convex superquadratic at zero infinity, then id="M10">\begin{document}$ T&gt;0 system possesses nonconstant id="M11">\begin{document}$ $\end{document}</tex-math></inline-formula>-cyclic orbit id="M12">\begin{document}$ belonging to id="M13">\begin{document}$ \{pT, \frac{pT}{p+1}\} For id="M14">\begin{document}$ R\left(-\frac{2\pi}{p}\right)^{\diamond n} id="M15">\begin{document}$ p large enough, id="M16">\begin{document}$ prescribed id="M17">\begin{document}$ period.</p>
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2022
ISSN: ['1553-5231', '1078-0947']
DOI: https://doi.org/10.3934/dcds.2022115