On Hamiltonian stable Lagrangian tori in complex hyperbolic spaces

Persistence of Hyperbolic Tori in Hamiltonian Systems

We generalize the well-known result of Graff and Zehnder on the persistence of hyperbolic invariant tori in Hamiltonian systems by considering non-Floquet, frequency varying normal forms and allowing the degeneracy of the unperturbed frequencies. The preservation of part or full frequency components associated to the degree of non-degeneracy is considered. As applications, we consider the persi...

BScan - lagrangian tori in projective spaces

Here we discuss the following situation. Consider CP with the standard symplectic form ω such that its cohomology class [ω] ∈ H(CP) is a generator of H(CP). It’s very well known, see f.e. [3], that the canonical class K of the projective space equals to −(n+1)[ω]. Consider the anticanonical line bundle K∗ → CP and fix a connection a on it such that the curvature form Fa is proportional to the s...

Remarks on the definition of hyperbolic tori of Hamiltonian systems

Maximal Hamiltonian tori for polygon spaces

We study the poset of Hamiltonian tori for polygon spaces. We determine some maximal elements and give examples where maximal Hamiltonian tori are not all of the same dimension.

Hamiltonian stationary Lagrangian tori contained in a hypersphere

The Clifford torus is a torus in a three-dimensional sphere. Homogeneous tori are simple generalization of the Clifford torus which still in a three-dimensional sphere. There is a way to construct tori in a threedimensional sphere using the Hopf fibration. In this paper, all Hamiltonian stationary Lagrangian tori which is contained in a hypersphere in the complex Euclidean plane are constructed...