Geodesics flows in singular metrics

• Grant number: 14/04944-6
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: September 01, 2014
• End date: August 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Farid Tari
• Grantee: Farid Tari
• Visiting researcher: Alexey Remizov
• Visiting researcher institution: École Polytechnique, France
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The research project contains problems which are connected with singularity theory, ordinary differential equations, differential geometry, and control theory. There is an interest in studying manifolds with singular metrics both in mathematics and in physics. In our research project, we concentrate on mathematical aspects of singular metrics, in particular, on singularities of geodesic flows and their behavior around the singular locus of the metric. We also propose to study singularities of geodesic flows in the Dirac problem and in singular Lagrangians. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

REMIZOV, A. O.; TARI, F.. Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics. Geometriae Dedicata, v. 185, n. 1, p. 131-153, DEC 2016. (14/04944-6, 14/00304-2)

REMIZOV, A. O.. GEODESICS IN GENERALIZED FINSLER SPACES: SINGULARITIES IN DIMENSION TWO. JOURNAL OF SINGULARITIES, v. 14, p. 22-pg., 2016-01-01. (14/04944-6)