Multiple brake orbits in $\mathbf{m}$-dimensional disks

Abstract

Let $(M,g)$ be a (complete) Riemannian surface, and let $\Omega \subset M$ be an open subset whose closure is homeomorphic to a disk. We prove that if $\partial \Omega$ is smooth and it satisfies a strong concavity assumption, then there are at least two distinct orthogonal geodesics in $\overline{\Omega }=\Omega \bigcup \partial \Omega$. Using the results given in [6], we then obtain a proof of the existence of two distinct brake orbits for a class of Hamiltonian systems. In our proof we shall use recent deformation results proved in [7].

26 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1003.3846

Cited by in corpus (1)

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