Geodesic
The absence of nonclosed Poisson-stable semitrajectories and trajectories doubly asymptotic to a double limit cycle for dynamical systems of the first degree of structural instability on orientable two-dimensional manifolds
Sbornik. Mathematics, Tome 5 (1968) no. 2, pp. 205-219

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In the present paper we investigate the absence, for dynamical systems of :he first degree of structural instability on two-dimensional compact orientable manifolds of any genus, of nonclosed Poisson-stable semitrajectories and trajectories that are doubly asymptotic to a double limit cycle. The propositions are some of the basic propositions that must be added to the known conditions for the first degree of structural instability on a plane (or sphere) [1] in order to obtain a description of dynamical systems of the first degree of structural instability on orientable two-dimensional manifolds. Systems of the first degree of structural instability on a torus were considered in [2]. A study of such systems on two-dimensional manifolds of higher genus has not been carried out up to the present time. 
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     author = {S. Kh. Aranson},
     title = {The absence of nonclosed {Poisson-stable} semitrajectories and trajectories doubly asymptotic to a double limit cycle for dynamical systems of the first degree of structural instability on orientable two-dimensional manifolds},
     journal = {Sbornik. Mathematics},
     pages = {205--219},
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     volume = {5},
     number = {2},
     year = {1968},
     language = {en},
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S. Kh. Aranson. The absence of nonclosed Poisson-stable semitrajectories and trajectories doubly asymptotic to a double limit cycle for dynamical systems of the first degree of structural instability on orientable two-dimensional manifolds. Sbornik. Mathematics, Tome 5 (1968) no. 2, pp. 205-219. http://geodesic.mathdoc.fr/item/SM_1968_5_2_a3/