Geodesic
Energy function for $\Omega$-stable flows without limit cycles on surfaces
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 21 (2019) no. 4, pp. 460-468.

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The paper is devoted to the study of the class of $\Omega$-stable flows without limit cycles on surfaces, i.e. flows on surfaces with non-wandering set consisting of a finite number of hyperbolic fixed points. This class is a generalization of the class of gradient-like flows, differing by forbiddance of saddle points connected by separatrices. The results of the work are the proof of the existence of a Morse energy function for any flow from the considered class and the construction of such a function for an arbitrary flow of the class. Since the results are a generalization of the corresponding results of K. Meyer for Morse-Smale flows and, in particular, for gradient-like flows, the methods for constructing the energy function for the case of this article are a further development of the methods used by K. Meyer, taking in sense the specifics of $\Omega$-stable flows having a more complex structure than gradient-like flows due to the presence of the so-called “chains” of saddle points connected by their separatrices.
Keywords: energy function, $\Omega$-stable flow, Morse function, a flow without limit cycles, a flow on a surface. 
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A. E. Kolobyanina; V. E. Kruglov. Energy function for $\Omega$-stable flows without limit cycles on surfaces. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 21 (2019) no. 4, pp. 460-468. http://geodesic.mathdoc.fr/item/SVMO_2019_21_4_a4/

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