Using the framework of metriplectic systems on Rn we will describe a constructive geometric method to add a dissipation term to a Hamilton-Poisson system such that any solution starting in aâ€¦ (More)

We will prove the equivalence of three methods, the so called energy methods, for establishing the stability of an equilibrium point for a dynamical system. We will illustrate by examples that thisâ€¦ (More)

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 conditionsâ€¦ (More)

As an important application of chaotic dynamical systems, chaos-based secure communication and cryptography attracted continuous interest over the last decade. It studies methods of controllingâ€¦ (More)

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 Lieâ€¦ (More)

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. Weâ€¦ (More)