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A ramified Cauchy problem for operators having Hamiltonian rest points. (English. Russian original) Zbl 0823.58034
Russ. Acad. Sci., Dokl., Math. 47, No. 3, 468-473 (1993); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 330, No. 3, 294-297 (1993).
From the text: “The object of this note is to study the propagation of singularities of the Cauchy problem for differential equations in a space of multiple-valued ramified functions. It is known that if the Hamiltonian vector field corresponding to the principal symbol of this equation does not vanish, then the singularities of the solutions are propagated along the projections onto configuration space of the trajectories of the corresponding vector field. However, if the Hamiltonian vector field contains rest points the situation is completely different”.
MSC:
58J47 Propagation of singularities; initial value problems on manifolds
32S35 Mixed Hodge theory of singular varieties (complex-analytic aspects)
32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
35A20 Analyticity in context of PDEs
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