Generalized action-angle coordinates in toric contact spaces

Abstract

In this paper we are concerned with completely integrable Hamiltonian systems in the setting of contact geometry. Unlike the symplectic case, contact structures are automatically Hamiltonian. Using the Jacobi brackets defined on contact manifolds, 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 toric Sasaki-Einstein spaces $T^{1,1}$ and $Y^{p,q}$.

12 pages, references added, typos fixed

References in corpus (6)

• Contact Hamiltonian Mechanics
• Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
• Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$
• Conformal Killing-Yano Tensors on Manifolds with Mixed 3-Structures
• Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits
• Integrability of geodesics and action-angle variables in Sasaki-Einstein space $T^{1,1}$