The main result of this paper is Theorem 2.13 which says that the quotient μ({1})/U associated to a quasi-hamiltonian space (M,ω, μ : M → U) has a symplectic structure even when 1 is not a regular value of the momentum map μ. Namely, it is a disjoint union of symplectic manifolds of possibly different dimensions, which generalizes the result of Alekseev, Malkin and Meinrenken in [AMM98]. We ill...

We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by means the adjoint representations algebras. In this way, we calculate some four dimensional and nilpotent six symplectic real groups. Then using Magri-Morosi's theorem obtain new bi-Hamiltonian systems with as phase spaces.

We give a classification of generic coadjoint orbits for the groups of symplectomorphisms and Hamiltonian diffeomorphisms of closed symplectic surfaces. We also classify simple Morse functions on symplectic surfaces with respect to actions of those groups. This gives an answer to V.Arnold’s problem on invariants of generic isovorticed fields for 2D ideal fluids.

We give a survey of infinite dimensional Hamiltonian systems with infinite dimensional Lie groups as symmetry groups and discuss concrete examples from soliton equations, plasma physics, fluid mechanics and quantum field theory. We present some new results of applications to BRST symmetries and g-symplectic structures.

We show how the theory of Poisson Lie groups can be used to establish the Poisson properties of the Yang-Baxter maps and related transfer dynamics. As an example we present the Hamiltonian structure for the matrix KdV soliton interaction.

in this research we described the effective hamiltonian theory and applied this theory to the calculation of current-current (q1,2) and qcd penguin (q3,…,6) c quark decay rates. we calculated the decay rates of semileptonic and hadronic of charm quark in the effective hamiltonian theory. we investigated the decay rates of d meson decays according to spectator quark model (sqm) for the calculati...

1Jerrold E. Marsden and Tudor S. Ratiu, Introduction to Mechanics and Symmetry, second ed., Chapter 2. 2Serge Lang, Differential and Riemannian Manifolds, p. 150, Theorem 8.1; Mircea Puta, Hamiltonian Mechanical Systems and Geometric Quantization, p. 12, Theorem 1.3.1. 3Andreas Kriegl and Peter W. Michor, The Convenient Setting of Global Analysis, p. 522, §48; Peter W. Michor, Some geometric ev...