Elena Gurevich
Bolshaya Pecherskaya 25/12, Nizhnii Novgorod, 603155, Russia
National Research University Higher School of Economics
Publications:
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Gurevich E. Y., Imaev R. R.
On Embedding of Separatrices of Morse – Smale Diffeomorphism on Manifolds of Dimension $n\geqslant 4$
2026, Vol. 22, no. 2, pp. 469-483
Abstract
We show that, for Morse – Smale diffemorphism $f\colon M^n\to M^n$, $n\geqslant 4$, the closure of one- and $(n-1)$-dimensional separatrices in a basin of a sink point $\omega$ forms a trivial frame that contrasts with the case $n=3$. This result is a first step in the solution of problems of topological classification, embedding in a flow and existence of energy functions for such diffeomorphisms.
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Grines V. Z., Gurevich E. Y., Zhuzhoma E. V., Zinina S. K.
Heteroclinic curves of Morse – Smale cascades and separators in magnetic field of plasma
2014, Vol. 10, No. 4, pp. 427-438
Abstract
We obtain properties of three-dimensional phase space and dynamics of Morse–Smale diffeomorphism that led to existence of at least one heteroclinical curve in non-wandering set of the diffeomorphism. We apply this result to solve a problem of existence of separators in magnetic field of plasma.
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