Displaying similar documents to “Bifurcation of periodic orbits of time dependent Hamiltonian systems on symplectic manifolds.”

Length minimizing Hamiltonian paths for symplectically aspherical manifolds

Ely Kerman, François Lalonde (2003)

Annales de l’institut Fourier

Similarity:

In this note we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of Polterovich and Schwarz, we study the role, in the Floer complex of the generating Hamiltonian, of the global extrema which remain fixed as the time varies. Our main result determines a natural condition which implies that the corresponding path minimizes the positive Hofer length. We use this to prove...

Singular Hamiltonian systems and symplectic capacities

Alfred Künzle (1996)

Banach Center Publications

Similarity:

The purpose of this paper is to develop the basics of a theory of Hamiltonian systems with non-differentiable Hamilton functions which have become important in symplectic topology. A characteristic differential inclusion is introduced and its equivalence to Hamiltonian inclusions for certain convex Hamiltonians is established. We give two counterexamples showing that basic properties of smooth systems are violated for non-smooth quasiconvex submersions, e.g. even the energy conservation...