Scientific articles

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

A. N. Kurbatskii^a, N. G. Pavlova^b, A. O. Remizov<sup>c

a</sup> 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.

UDC: 514

Received: 03.04.2017

DOI: 10.20310/1810-0198-2017-22-3-539-551