Object's details: Multiple connecting geodesics of a Randers-Kropina metric via homotopy theory for solutions of an affine control system

Provider:Akademicka Platforma Czasopism

Description

Title:
Multiple connecting geodesics of a Randers-Kropina metric via homotopy theory for solutions of an affine control system
Creator:
Caponio, Erasmo;
Javaloyes, Miguel Angel;
Masiello, Antonio
Description:
We consider a geodesic problem in a manifold endowed with a Randers-Kropina metric. This is a type of a singular Finsler metric arising both in the description of the lightlike vectors of a spacetime endowed with a causal Killing vector field and in the Zermelo's navigation problem with a wind represented by a vector field having norm not greater than one. By using Lusternik-Schnirelman theory, we prove existence of infinitely many geodesics between two given points when the manifold is not contractible. Due to the type of non-holonomic constraints that the velocity vectors must satisfy, this is achieved thanks to some recent results about the homotopy type of the set of solutions of an affine control system associated with a totally non-integrable distribution.
Object availability:
free access
Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
Prawa autorskie (c) 2023 Erasmo Caponio, Miguel Angel Javaloyes, Antonio Masiello
Date:
2023.02.26
Type:
info:eu-repo/semantics/article;
info:eu-repo/semantics/publishedVersion;
Recenzowany artykuł
Language:
English
Source:
Topological Methods in Nonlinear Analysis; Vol 61, No 1 (March 2023); 527 - 547;
1230-3429
Publisher:
Nicolaus Copernicus University in Toruń
Relation: https://apcz.umk.pl/TMNA/article/view/42826/34994 ;https://apcz.umk.pl/TMNA/article/view/42826/34995
Subject:
Randers metric;
Kropina metric;
geodesics;
affine control systems;
causal Killing field;
Zermelo's navigation problem;
Primary: 58E10, 53C22, 53C60;
Secondary: 34H05
Identifier: https://apcz.umk.pl/TMNA/article/view/42826
Data provider:
Akademicka Platforma Czasopism

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