We prove, under a pinching hypothesis, a theorem of existence ofat least n periodic orbits for a closed regular energy hypersurface$\Sigma$ in $\mathbb{R}^{2n}$ which is the level set of a natural (i.e. of the type "potential + kinetic energy") Hamiltonian function and projects onto a potential well in the configuration space.
We prove, under a pinching hypothesis, a theorem of existence of at least n periodic orbits for a closed regular energy hypersurface Σ in R2 n which is the level set of a natural (i.e. of the type "potential + kinetic energy") Hamiltonian function and projects onto a potential well in the configuration space. © 2008 Elsevier Inc. All rights reserved.
Existence of multiple periodic solutions for a natural Hamiltonian system in a potential well / Villarini, Massimo. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 246:3(2009), pp. 1207-1234. [10.1016/j.jde.2008.08.003]
Existence of multiple periodic solutions for a natural Hamiltonian system in a potential well
VILLARINI, Massimo
2009
Abstract
We prove, under a pinching hypothesis, a theorem of existence of at least n periodic orbits for a closed regular energy hypersurface Σ in R2 n which is the level set of a natural (i.e. of the type "potential + kinetic energy") Hamiltonian function and projects onto a potential well in the configuration space. © 2008 Elsevier Inc. All rights reserved.
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