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Article

Гетероклинические кривые градиентно-подобных диффеоморфизмов и топология несущего многообразия.

In the study of deterministic processes described by the Morse-Smale systems noncompact heteroclinic curves play special role. These curves belong to intersections of stable and unstable manifolds of saddle periodic points. In particular, these curves are mathematical models of magnetic separators in the plasma eld. We consider the class of gradient-like dieomorphisms on three-dimensional manifolds such that their periodic points and a part of their invariant manifolds form disjoint tamely embedded surfaces. We prove that the number of the surfaces is nite and all of them have the same genus. The main result is presentation of the exact lower estimation for the number of heteroclinic curves of any dieomorphism from considered class. This estimation is dened by genus of surfaces and their number. In addition the paper describes the topological type of manifolds which admit considered dieomorphisms.