Integrability and geometric prequantization of the Maxwell-Bloch equations

AbstractIn this paper we discuss the integrability and geometric prequantization of the 3-dimensional real valued Maxwell-Bloch equations and point out some of their properties

Symmetry breaking for toral actions in simple mechanical systems

For simple mechanical systems, bifurcating branches of relative equilibria with trivial symmetry from a given set of relative equilibria with toral symmetry are found. Lyapunov stability conditions along these branches are given.Comment: 25 page

A short proof of chaos in an atmospheric system

We will prove the presence of chaotic motion in the Lorenz five-component atmospheric system model using the Melnikov function method developed by Holmes and Marsden for Hamiltonian systems on Lie Groups.Comment: PACS: 02.20.Sv; 02.30.Hg; 02.40.-k; 92.60.-e. 5 page

Periodic orbits in the case of a zero eigenvalue

We will show that if a dynamical system has enough constants of motion then a Moser-Weinstein type theorem can be applied for proving the existence of periodic orbits in the case when the linearized system is degenerate.Comment: 6 pages, no figure

Asymptotic Stability for a Class of Metriplectic Systems

Using the framework of metriplectic systems on $\R^n$ we will describe a constructive geometric method to add a dissipation term to a Hamilton-Poisson system such that any solution starting in a neighborhood of a nonlinear stable equilibrium converges towards a certain invariant set. The dissipation term depends only on the Hamiltonian function and the Casimir functions

On the symmetry breaking phenomenon

We investigate the problem of symmetry breaking in the framework of dynamical systems with symmetry on a smooth manifold. Two cases will be analyzed: general and Hamiltonian dynamical systems. We give sufficient conditions for symmetry breaking in both cases