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Tambov University Reports. Series: Natural and Technical Sciences, 2017, Volume 22, Issue 3, Pages 539–551 (Mi vtamu111)  

Singularities of geodesic flows and lines in pseudo-Finsler spaces. III

A. N. Kurbatskiia, N. G. Pavlovab, A. O. Remizovc

a Moscow State (Lomonosov) University, Moscow School of Economics
b RUDN University
c V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

Abstract: This is a third paper in the series devoted to singularities of geodesic flows in generalized Finsler (pseudo-Finsler) spaces. In two previous papers, we defined geodesics as extremals of a certain auxiliary functional whose non-isotropic extremals coincide with extremals of the action functional, and studied generic singularities of so-defined geodesic flows in the case the pseudo-Finsler metric is given by a generic form of degree 3 on a two-dimensional manifold. In the present paper, we consider an important non-generic case: singularities of geodesic flows on two-dimensional surfaces embedded into the Berwald-Moor space of arbitrary dimension.

Keywords: Pseudo-Finsler spaces, Berwald-Moor metric, geodesics, singular points, resonances, normal forms.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00766
17-01-00849
Grant of the President of the Russian Federation НШ-8215.2016.1
The work is partially supported by the Russian Fund for Basic Research (projects 16-01-00766, 17-01-00849) and the grant of the Russian Federation President for the state support of leading scientific schools № NSh-8215.2016.1.


DOI: https://doi.org/10.20310/1810-0198-2017-22-3-539-551

References: PDF file   HTML file

UDC: 514
Received: 03.04.2017

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