Periodic solutions of second order hamiltonian systems bifurcating from infinity
Periodic Solutions of Second Order Nonautonomous Systems with the Potentials Changing Sign
Some existence and multiplicity results for periodic solutions of second order nonautonomous systems with the potentials changing sign are presented. The proofs of the existence results rely on the use of a linking theorem and the Mountain Pass theorem by Ambrosetti and Rabinowitz [2]. The multiplicity results are deduced by the study of constrained critical points of minimum or Mountain Pass type.
Periodic solutions of some problems of 3-body type
Periodic Solutions on hypersurfaces and a result by C. Viterbo.
Periodic solutions with prescribed minimal period for convex autonomous hamiltonian systems.
Persistence of homoclinic tangencies for area-preserving maps
Persistent homoclinic tangencies and the unfolding of cycles
Perturbation results for a class of singular Hamiltonian systems
The existence of solutions with prescribed period for a class of Hamiltonian systems with a Keplerian singularity is discussed.
Perturbazioni periodiche di equazioni differenziali ordinarie su varietà differenziabili
Poincaré renormalized forms
Poincaré-Melnikov theory for n-dimensional diffeomorphisms
We consider perturbations of n-dimensional maps having homo-heteroclinic connections of compact normally hyperbolic invariant manifolds. We justify the applicability of the Poincaré-Melnikov method by following a geometric approach. Several examples are included.
Polynomial systems: a lower bound for the weakened 16th Hilbert problem.
In this paper we provide the greatest lower bound about the number of (non-infinitesimal) limit cycles surrounding a unique singular point for a planar polynomial differential system of arbitrary degree.
Problèmes de modules pour des équations différentielles non linéaires du premier ordre
Properties of Pseudo-holomorphic Curves in Symplectisations II: Embedding Controls and Algebraic Invariants.
Quadratic vector fields in the plane have a finite number of limit cycles
Quelques Commentaires Sur Le Plongement Des Difféomorphismes Locaux Du Plan.
Recent results on the separatrix splitting for the standard map
Remarks on dynamical systems with weak forces.
Resurgence in a Hamilton-Jacobi equation
We study the resurgent structure associated with a Hamilton-Jacobi equation. This equation is obtained as the inner equation when studying the separatrix splitting problem for a perturbed pendulum via complex matching. We derive the Bridge equation, which encompasses infinitely many resurgent relations satisfied by the formal solution and the other components of the formal integral.
Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems
We propose a new rigorous numerical technique to prove the existence of symmetric homoclinic orbits in reversible dynamical systems. The essential idea is to calculate Melnikov functions by the exponential dichotomy and the rigorous numerics. The algorithm of our method is explained in detail by dividing into four steps. An application to a two dimensional reversible system is also treated and the existence of a symmetric homoclinic orbit is rigorously verified as an example.