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 nonlinear two-species oscillatory system: bifurcation and stability analysis.
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...
A study of the Rimmer bifurcation of symmetric fixed points of reversible diffeomorphisms.
A subshift of finite type in the Takens-Bogdanov bifurcation with symmetry.
A sufficient condition for the existence of multiple periodic solutions of differential inclusions
A Viterbo-Hofer-Zehnder type result for hamiltonian inclusions
Abelian integrals for quadratic vector fields.
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.
Abelian integrals related to Morse polynomials and perturbations of plane hamiltonian vector fields
Let be the real vector space of Abelian integralswhere is a fixed real polynomial, is an arbitrary real polynomial and , , is the interior of the oval of which surrounds the origin and tends to it as . We prove that if is a semiweighted homogeneous polynomial with only Morse critical points, then is a free finitely generated module over the ring of real polynomials , and compute its rank. We find the generators of in the case when is an arbitrary cubic polynomial. Finally we...
About some theorems by L. P. Šil'nikov