Lie Groups Analysis and Contact Transformations for Ito System

Lattices in contact Lie groups and 5-dimensional contact solvmanifolds

This paper investigates the geometry of compact contact manifolds that are uniformized by contact Lie groups, i.e., manifolds of the form Γ \ G for some Lie group G with a left invariant contact structure and uniform lattice Γ ⊂ G. We re-examine Alexander’s criteria for existence of lattices on solvable Lie groups and apply them, along with some other well known tools. In particular, we restric...

Left Invariant Contact Structures on Lie Groups

A result from Gromov ensures the existence of a contact structure on any connected non-compact odd dimensional Lie group. But in general such structures are not invariant under left translations. The problem of finding which Lie groups admit a left invariant contact structure (contact Lie groups), is then still wide open. We perform a ‘contactization’ method to construct, in every odd dimension...

On Contact and Symplectic Lie Algeroids

In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by m...

On Certain Groups of Birational Contact Transformations*

Lie groups and error analysis

A new approach to error analysis is introduced, based on the observation that many numerical procedures can be interpreted as computations of products in a suitable Lie group. The absence of an additive error law for such procedures is intimately related to the nonexistence of bi-invariant metrics on the relevant groups. Introducing the notion of an almost Inn(G) invariant metric (a left invari...