Abstracts

Mihai Visinescu

Complete integrability in toric contact geometry

We describe the completely integrable Hamiltonian systems in the setting of contact geometry. Unlike the symplectic case, contact structures are automatically Hamiltonian. Choosing a contact one-form \eta, the function \eta(X) is called the contact Hamiltonian associated to the contact vector field X. It is convenient to choose the function \eta(R_{\eta}) = 1 as the Hamiltonian, making the Reeb vector field R_{\eta} the Hamiltonian vector field. Using the Jacobi bracket defined on a contact manifold, we discuss the commutativity of the first integrals for contact Hamiltonian systems and introduce the generalized contact action-angle variables. We exemplify the general scheme in the case of the five-dimensional T^{1,1} and Y^{p,q} Sasaki-Einstein spaces.

References:

[1] M. Visinescu, Eur. Phys. J. C 76, 498 (2016).
[2] M. Visinescu, Prog. Theor. Exp. Phys. 2017, 013A01 (2017).
[3] M. Visinescu, arXiv:1704.04034.