Geodesics in generalized Finsler spaces: singularities in dimension two

Journal of Singularities
volume 14 (2016), 172-193

Received: 18 February 2016. Received in revised form: 31 August 2016.

DOI: 10.5427/jsing.2016.14j

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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 us to consider isotropic lines as (unparametrized) geodesics.

Keywords:

Finsler spaces and generalizations; geodesics; singular points; normal forms

2010 Mathematical Subject Classification:

53B40 (Primary), 53C22, 34C05

Author(s) information:

Alexey Remizov
Instituto de Ciências Matemáticas e de Computação-USP
Avenida Trabalhador São-Carlense, 400 - Centro
CEP: 13566-590 - São Carlos - SP
Brazil
email: alexey-remizov@yandex.ru