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

2012/03/23 by R. Giambò, Roberto Giambò, Fabio Giannoni +6
Engineering · Mathematics · #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Hydraulic Fracturing and Reservoir Analysis #Hydrocarbon exploration and reservoir analysis #math.DS

paper · pdf · doi:10.48550/arxiv.1203.5198

withdrawal reason: crucial technical result (Lemma 2.2) is incorrect

openalex publication_date 2012/03/23 · arxiv created 2012/07/19 · arxiv updated 2014/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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