On some invariants of dynamical systems on two-dimensional manifolds (necessary and sufficient conditions for the topological equivalence of transitive dynamical systems)

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.
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