Griffiths, Phillip A. Linearizing flows and a cohomological interpretation of Lax equations. (English) Zbl 0585.58028 Am. J. Math. 107, 1445-1484 (1985). The author considers a Lax equation of the type \(dA(\xi,t)/dt=[B(\xi,t),A(\xi,t)]\) (\(\xi\) is a rational parameter) and associates to it an algebraic curve (its spectral curve) together with a dynamical system \(L_ t\) on its Jacobian variety J(C). He gives necessary and sufficient conditions on B for the flow \(t\to L_ t\) to be linear on J(C). These conditions are cohomological: the Lax equations turn out to have a very natural cohomological interpretation. Reviewer: Yu.E.Gliklikh Cited in 3 ReviewsCited in 36 Documents MSC: 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37C10 Dynamics induced by flows and semiflows Keywords:linearizing flows; cohomology; Lax equation; algebraic curve; Jacobian variety PDFBibTeX XMLCite \textit{P. A. Griffiths}, Am. J. Math. 107, 1445--1484 (1985; Zbl 0585.58028) Full Text: DOI Link