4 Recherche d'orbites périodiques d'un champ hamiltonien associé à une structure symplectique non standard
A "Birkhoff-Lewis" type result for a class of Hamiltonian systems.
A construction of realizations of perturbations of Poincaré maps
A criterion for the non-existence of invariant circles
A generalization of the Weinstein-Moser theorems on periodic orbits of a hamiltonian system near an equilibrium
A geometric approach to a result of Benci and Giannoni for Hamiltonian systems with singular potentials.
A global analysis of Newton iterations for determining turning points
The global convergence of a direct method for determining turning (limit) points of a parameter-dependent mapping is analysed. It is assumed that the relevant extended system has a singular root for a special parameter value. The singular root is clasified as a (i.e., as a turning point). Then, the Theorz for Imperfect Bifurcation offers a particular scenario for the split of the singular root into a finite number of regular roots (turning points) due to a given parameter imperfection. The relationship...
A Hopf Bifurcation Theorem for Difference Equations Approximating a Differential Equation.
A new chaotic attractor from 2D discrete mapping via border-collision period-doubling scenario.
A new degree for -invariant gradient mappings and applications
A new obstruction to embedding Lagrangian tori.
A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.
Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application to saddle connections and also to various subharmonics. The singular perturbation is unusual in that it uses...
A study of the Rimmer bifurcation of symmetric fixed points of reversible diffeomorphisms.
A sufficient condition for the existence of multiple periodic solutions of differential inclusions
A Viterbo-Hofer-Zehnder type result for hamiltonian inclusions
Abelian integrals of quadratic Hamiltonian vector fields with an invariant straight line.
We prove that the lowest upper bound for the number of isolated zeros of the Abelian integrals associated to quadratic Hamiltonian vector fields having a center and an invariant straight line after quadratic perturbations is one.
About some theorems by L. P. Šil'nikov
Absolute Stability and Bifurcation Theory.
An analogue to the Smale-Birkhoff homoclinic theorem for iterated entire mappings. (Summary).
An analogue to the Smale-Birkhoff homoclinic theorem for iterated entire mappings.