Geodesic
On~some invariants of dynamical systems on two-dimensional manifolds (necessary and sufficient conditions for the topological equivalence of transitive dynamical systems)
Sbornik. Mathematics, Tome 19 (1973) no. 3, pp. 365-393

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In this paper, topological invariants of dynamical systems given on a two-dimensional manifold $M^2$ of genus $p>1$ are selected which allow one to distinguish topologically inequivalent systems which have nonclosed, Poisson stable trajectories and non-null-homotopic closed trajectories. A necessary and sufficient condition for the topological equivalence of transitive dynamical systems on $M^2$ is established. Figures: 6. Bibliography: 20 titles. 
@article{SM_1973_19_3_a1,
     author = {S. Kh. Aranson and V. Z. Grines},
     title = {On~some invariants of dynamical systems on two-dimensional manifolds (necessary and sufficient conditions for the topological equivalence of transitive dynamical systems)},
     journal = {Sbornik. Mathematics},
     pages = {365--393},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_19_3_a1/}
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S. Kh. Aranson; V. Z. Grines. On~some invariants of dynamical systems on two-dimensional manifolds (necessary and sufficient conditions for the topological equivalence of transitive dynamical systems). Sbornik. Mathematics, Tome 19 (1973) no. 3, pp. 365-393. http://geodesic.mathdoc.fr/item/SM_1973_19_3_a1/