Abstract
The Landau-Lifschitz equations describe the time evolution of magnetization in classical ferromagnets and are of basic importance for the understanding of magnetism. Under quite general conditions, we have shown that dissipative versions of these equations have attracting sets which are finite dimensional in a suitable sense. It follows from these results that, after an initial transient period, only a finite number of spin-wave modes contribute to the spin-wave instabilities responsible for the chaotic behavior recently found in ferromagnetic resonance (“spin-wave turbulence”), in both the transverse and parallel pumping versions. The physical significance of the “global attractor” is mentioned, and estimates of upper and lower bounds for its dimension are discussed. The numerical estimates of this dimension are very large, and physical reasons for this circumstance are discussed.
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Gill, T.L., Zachary, W.W. (1989). The global attractor for the Landau-Lifschitz equations. In: Maclin, A.P., Gill, T.L., Zachary, W.W. (eds) Magnetic Phenomena. Lecture Notes in Physics, vol 337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020701
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DOI: https://doi.org/10.1007/BFb0020701
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