Homoclinic and periodic orbits for hamiltonian systems
We consider a conservative second order Hamiltonian system in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ 0 = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.
This work uses a variational approach to establish the existence of at least two homoclinic solutions for a family of singular Newtonian systems in ℝ³ which are subjected to almost periodic forcing in time variable.
In this note we prove the stability of the Gieseker point of an irreducible homogeneous bundle over a rational homogeneous space. As an application we get a sharp upper estimate for the first eigenvalue of the Laplacian of an arbitrary Kähler metric on a compact Hermitian symmetric spaces of ABCD–type.
A Finsler geometry may be understood as a homogeneous variational problem, where the Finsler function is the Lagrangian. The extremals in Finsler geometry are curves, but in more general variational problems we might consider extremal submanifolds of dimension . In this minicourse we discuss these problems from a geometric point of view.
Un sous-ensemble pfaffien d’un ouvert semi-analytique est une intersection finie d’ensembles semi-analytiques relativement compacts de et de feuilles non spiralantes de certains feuilletages analytiques de codimension 1 de Les sous-ensembles semi-pfaffiens de sont les éléments de la plus petite classe de sous-ensembles de contenant les sous-ensembles pfaffiens de , stable par intersection finie, réunion finie et différence symétrique. Les ensembles -pfaffiens sont les éléments de la...