A variational approach to chaotic dynamics in periodically forced nonlinear oscillators
A variational construction of chaotic trajectories for a Hamiltonian system on a torus
A geometric criterion for the existence of chaotic trajectories of a Hamiltonian system with two degrees of freedom and the configuration space a torus is given. As an application, positive topological entropy is established for a double pendulum problem.
Homoclinic orbits for an almost periodically forced singular Newtonian system in ℝ³
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.
On a deformed version of the two-disk dynamo system
We give some deformations of the Rikitake two-disk dynamo system. Particularly, we consider an integrable deformation of an integrable version of the Rikitake system. The deformed system is a three-dimensional Hamilton-Poisson system. We present two Lie-Poisson structures and also symplectic realizations. Furthermore, we give a prequantization result of one of the Poisson manifold. We study the stability of the equilibrium states and we prove the existence of periodic orbits. We analyze some properties...
Quadratic systems with homoclinic cycles described by quintic curves.