Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural Hamiltonian systems
- 1 October 1984
- journal article
- Published by European Mathematical Society - EMS - Publishing House GmbH in Annales de l'Institut Henri Poincaré C, Analyse non linéaire
- Vol. 1 (5) , 401-412
- https://doi.org/10.1016/s0294-1449(16)30420-6
Abstract
We prove that the Hamiltonian system \begin{cases} \.{p}\: = \:−\frac{∂\mathrm{V}}{∂q} \\ \.{q}\: = \:p \end{cases} \qquad p,\:q \in \mathrm{R}^{n};\ \mathrm{V} \in \mathrm{C}^{2}\left(\mathrm{R}^{n}\right) has at least one periodic solution of energy h , provided that the set \{q \in \mathrm R^n | \mathrm V(q) ⩽ h\} is compact.This publication has 6 references indexed in Scilit:
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