Work

Positive topological entropy for semi-Riemannian geodesic flows

Year: 2025

Type: article

Abstract: We consider a semi-Riemannian metric whose associated geodesic flow either contains a non-hyperbolic periodic orbit or has infinitely many hyperbolic periodic orbits. Under some conditions, we show that the metric can be C 2 C^2 -perturbed such that the geodesic flow exhibits positive topological entropy, there are infinitely many non-lightlike closed geodesics, and their number grows exponentially with respect to the length.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17337

Authors: Mário Bessa, João Lopes Dias, Pedro Matias, Maria Torres

Institutions: Universidade Aberta, Universidade Lusófona, Centro de Matemática, University of Minho

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Fundação para a Ciência e a Tecnologia

Award: Research in Economics and Mathematics