Index theory revealed its outstanding role in the study of periodic orbits of Hamiltonian
systems and the dynamical consequences of this theory are enormous. Although the index …

(2) In the Lorentzian case, causality theory is a specific tool fully adapted to its particularities.
So, other sophisticated theories which may work in the Riemannian case, must be …

Perturbed geodesics are trajectories of particles moving on a semi-Riemannian manifold in
the presence of a potential. Our purpose here is to extend to perturbed geodesics on semi …

In this paper, we derive the first and the second variation of the energy functional for a
pseudo-Finsler metric using the family of affine connections associated to the Chern …

It is well known that the linear stability of the Lagrangian elliptic solutions in the classical
planar three-body problem depends on a mass parameter β and on the eccentricity e of the …

Given a one-parameter family of semi Riemannian metrics on an n-dimensional manifold M,
a family of time-dependent potentials $\mu (\sigma_b) $ are different. If the data are analytic …

We develop an index theory for parabolic and collision solutions to the classical n-body
problem and we prove sufficient conditions for the finiteness of the spectral index valid in a …

Heteroclinic orbits for one-parameter families of nonautonomous vectorfields appear in a
very natural way in many physical applications. Inspired by a recent bifurcation result for …

In this paper we provide a sufficient condition for the linear instability of a periodic orbit for a
free period Lagrangian system on a Riemannian manifold. The main result establish a …

In this paper we shall use the abstract bifurcation theorems developed by the author in
previous papers to study bifurcations of solutions for Lagrangian systems on manifolds …