Geodesics in generalized Finsler spaces: singularities in dimension two

TL;DR

This paper investigates the behavior of geodesics and their singularities in two-dimensional generalized Finsler spaces, providing insights into their structure and properties through a novel approach involving auxiliary functionals.

Contribution

It introduces a new method to analyze geodesics in pseudo-Finsler spaces using an auxiliary functional, enabling the study of isotropic lines as geodesics.

Findings

Identification of singularities in geodesic flows

Characterization of isotropic lines as geodesics

Development of a framework for analyzing pseudo-Finsler geodesics

Abstract

We study singularities of geodesics flows in two-dimensional generalized Finsler spaces (pseudo-Finsler spaces). Geodesics are defined as extremals of a certain auxiliary functional whose non-isotropic extremals coincide with extremals of the action functional. This allows to consider isotropic lines as (unparametrized) geodesics.