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A characterization of isochronous centres in terms of symmetries.

Emilio Freire, Gasull, Armengol, Guillamon, Antoni 2 (2004)

Revista Matemática Iberoamericana

We present a description of isochronous centres of planar vector fields X by means of their groups of symmetries. More precisely, given a normalizer U of X (i.e., [X,U]= µ X, where µ is a scalar function), we provide a necessary and sufficient isochronicity condition based on µ. This criterion extends the result of Sabatini and Villarini that establishes the equivalence between isochronicity and the existence of commutators ([X,U]= 0). We put also special emphasis on the mechanical aspects of isochronicity;...

A functional analysis approach to Arnold diffusion

Massimiliano Berti, Philippe Bolle (2002)

Annales de l'I.H.P. Analyse non linéaire

A new method for measuring the splitting of invariant manifolds

David Sauzin (2001)

Annales scientifiques de l'École Normale Supérieure

A variational approach to homoclinic orbits in Hamiltonian systems.

Vittorio Coti Zelati, Ivar Ekeland, Eric Séré (1990)

Mathematische Annalen

A variational construction of chaotic trajectories for a Hamiltonian system on a torus

S. V. Bolotin, P. H. Rabinowitz (1998)

Bollettino dell'Unione Matematica Italiana

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.

An existence result on periodic solutions of an ordinary $p$ -Laplacian system.

Zhang, Xingyong, Zhou, Peixiang (2011)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Approximative sequences and almost homoclinic solutions for a class of second order perturbed Hamiltonian systems

Marek Izydorek, Joanna Janczewska (2014)

Banach Center Publications

In this work we will consider a class of second order perturbed Hamiltonian systems of the form $q ̈ + V_{q} (t, q) = f (t)$ , where t ∈ ℝ, q ∈ ℝⁿ, with a superquadratic growth condition on a time periodic potential V: ℝ × ℝⁿ → ℝ and a small aperiodic forcing term f: ℝ → ℝⁿ. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods. These approximative systems admit periodic solutions, and an almost homoclinic solution for the original system is obtained...