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arXiv · 1203.5198

Potential wells with a unique brake orbit. Counterexamples to a conjecture by H. Seifert

R. Giambò·F. Giannoni·P. Piccione
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Abstract

In this paper we prove the existence of real-analytic natural Hamiltonian systems - i.e. where H(q,p)=T(q,p)+V(q) in the 2N-dimensional real space, where N is any integer greater than 1 - with non critical energy levels E for the potential V such that the sublevel E of V is homeomorphic to the N-dimensional disk, and that only one brake orbit of energy E exists. A famous conjecture formulated by H. Seifert in 1948 claimed the existence of at least N distinct brake orbits for this situation.

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R. Giambò, F. Giannoni, P. Piccione. 2012-07-19. Potential wells with a unique brake orbit. Counterexamples to a conjecture by H. Seifert. https://arxiv.org/abs/1203.5198

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