Contact Hamiltonian systems

Contact and non-contact type Hamiltonian systems generated by second-order Lagrangians

We show that some very naturally occurring energymanifolds that are induced by second-order Lagrangians L = L(u, u′, u′′) are not, in general, of contact type in (R4, ω). We also comment on the more general question whether there exist any contact forms on these energy manifolds for which the associated Reeb vector field coincides with the Hamiltonian vector field.

Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S × S

I begin by giving a general discussion of completely integrable Hamiltonian systems in the setting of contact geometry. We then pass to the particular case of toric contact structures on the manifold S2×S3. In particular we give a complete solution to the contact equivalence problem for a class of toric contact structures, Y , discovered by physicists in [GMSW04a, MS05, MS06] by showing that Y ...

Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S 2 × S 3 ?

I begin by giving a general discussion of completely integrable Hamiltonian systems in the setting of contact geometry. We then pass to the particular case of toric contact structures on the manifold S × S. In particular we give a complete solution to the contact equivalence problem for a class of toric contact structures, Y , discovered by physicists by showing that Y p,q and Y p ′,q′ are ineq...

Real Hamiltonian forms of Hamiltonian systems

We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a given involution. The resulting subspace is isomorphic (but not symplectomorphic) to the initial phase space. Thus to each real Hamiltonian system we are able t...

Holomorphic Curves and Hamiltonian Systems in an Open Set with Restricted Contact-type Boundary