Potential wells with a unique brake orbit. Counterexamples to a conjecture by H. Seifert
Dynamical Systems
2014-06-04 v2
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.
Keywords
Cite
@article{arxiv.1203.5198,
title = {Potential wells with a unique brake orbit. Counterexamples to a conjecture by H. Seifert},
author = {R. Giambò and F. Giannoni and P. Piccione},
journal= {arXiv preprint arXiv:1203.5198},
year = {2014}
}
Comments
withdrawal reason: crucial technical result (Lemma 2.2) is incorrect