Using the relativistic Fermat's principle, we establish a bridge between stationary–complete
manifolds which satisfy the observer-manifold condition and pre-Randers metrics, namely …

A geodesic flower is a finite collection of geodesic loops based at the same point 𝑝 that
satisfy the following balancing condition: the sum of all unit tangent vectors to all geodesic …

In this paper we prove new upper bounds for the length of a shortest closed geodesic,
denoted $ l (M) $, on a complete, non-compact Riemannian surface $ M $ of finite area $ A …

We give a Morse-theoretic characterization of simple closed geodesics on Riemannian 2-
spheres. On any Riemannian 2-sphere endowed with a generic metric, we show there exists …

We show that, on a complete and possibly non-compact Riemannian manifold of dimension
at least 2 without close conjugate points at infinity, the existence of a closed geodesic with …

Neste trabalho estudamos dois problemas clássicos da geometria diferencial, a conexidade
geodésica em variedades afins e de Lorentz e a existência de geodésicas tipo-tempo …

This memoir, which I am presenting for my French habilitationa diriger des recherches, is a
promenade along the path that I followed as a researcher since my Ph. D. Its subject is the …

In this paper, we give multiple situations when having one or two geometrically distinct
closed geodesics on a complete Riemannian cylinder, a complete Möbius band or a …

In this thesis, we are studying topological and dynamical conditions imposing infinitely many
periodic orbits for some dynamical systems. In a first part, weelaborate on theories of …