A topological classification of integrable geodesic flows on the two-dimensional sphere with an additional integral quadratic in the momenta

Autor:	L. S. Polyakova, T. Z. Nguyen
Rok vydání:	1993
Předmět:	Pure mathematics Conjecture Integrable system Geodesic Applied Mathematics Mathematical analysis Geodesic map General Engineering Hamiltonian system Quadratic equation Flow (mathematics) Modeling and Simulation Metric (mathematics) Mathematics::Differential Geometry Mathematics
Zdroj:	Journal of Nonlinear Science. 3:85-108
ISSN:	1432-1467 0938-8974
Popis:	The analytic expression for a Riemannian metric on a 2-sphere, having integrable geodesic flow with an additional integral quadratic in momenta, is given in [Ko1]. We give the topological classification, up to topological equivalence of Liouville foliations, of all such metrics. The classification is computable, and the formula for calculating the complexity of the flow is straightforward. We prove Fomenko's conjecture that, from the point of view of complexity, the integrable geodesic flows with an additional integral linear or quadratic in momenta exhaust “almost all” integrable geodesic flows on the 2-dimensional sphere.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::082ac28d9e8d24adbae339ad9505ab04 https://doi.org/10.1007/bf02429860 Zobrazit plný text záznamu Full text from SpringerLink