Nonlinear Phenomena in Complex Systems, 2008, Vol.11, No.2, pp.269-273

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2008, Vol.11, No.2, pp.269-273

Criteria for Large-Scale Chaos in The Problem of Homogeneous Magnetization.
G. Voyatzis, S. Ichtiaroglou, and E. Meletlidou

We consider the Hamiltonian system derived from spatially homogenious solutions of the Landau-Lifshitz-Gilbert equation for the macroscopic magnetization of the ferromagnetic system without damping. The static field also breaks the plane symmetry S_z-S_z. We find the continued periodic orbits from the unperturbed integrable part to the perturbed system, with the help of first order perturbation theory. By transforming the one degree of freedom time dependent system into a two degree of freedom system and with the help of second order perturbation theory we predict the continuation of extra periodic orbits. We also find the stability of the continued periodic orbits of the first order perturbation theory. We finally find the value of the perturbative parameter where the main resonances overlap end therefore global chaos appears.
Key words: macroscopic magnetization, hamiltonian systems, continuation of periodic orbits, overlapping of resonances

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