Singularities of integrable geodesic flows on multidimensional torus and sphere
type: Item
instance of: scholarly article
title: Singularities of integrable geodesic flows on multidimensional torus and sphere
zbMATH Open document ID: 0849.58053
DOI: 10.1016/0393-0440(95)00008-9
author: Nguyen Tien Zung
published in: Journal of Geometry and Physics
publication date: 1996-11-10T00:00:00Z
review text: The author investigates geodesic flows of Liouville metrics on the torus \(T^n\) and of standard metrics on the sphere \(S^n\) (and their perturbations). These flows are integrable and it is assumed that first integrals are independent almost everywhere and their common level sets are compact. Thus, an associated singular foliation by Liouville tori appears. A germ of the foliation near a singular leaf is called a nonlocal singularity. The paper presents a topological description of nonlocal singularities for the considered geodesic flows.
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
zbMATH DE Number: 866114
zbMATH Keywords: geodesic flows
zbMATH Keywords: Liouville metrics
zbMATH Keywords: torus
zbMATH Keywords: sphere
zbMATH Keywords: singularities
reviewed by: Yu. N. Bibikov
MaRDI profile type: Publication
full work available at URL: 0393-0440(95)00008-9
OpenAlex ID: W2091495982
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description: scientific article; zbMATH DE number 866114