Multiple connecting geodesics of a Randers-Kropina metric via homotopy theory for solutions of an affine control system
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Published:2023-02-26
Issue:
Volume:
Page:1-21
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ISSN:1230-3429
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Container-title:Topological Methods in Nonlinear Analysis
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language:
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Short-container-title:TMNA
Author:
Caponio ErasmoORCID,
Javaloyes Miguel AngelORCID,
Masiello AntonioORCID
Abstract
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.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University
Subject
Applied Mathematics,Analysis
Cited by
1 articles.
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