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  • Комбинаторный инвариант для поверхностных диффеоморфизмов Морса-Смейла с ориентируемой гетероклиникой

Article

Комбинаторный инвариант для поверхностных диффеоморфизмов Морса-Смейла с ориентируемой гетероклиникой

In the present paper, we consider the class of orientation-preserving Morse-Smale diffeomorphisms f defined on an orientable surface M2. The work of A. A. Beznezhennykh and V. Z. Grines showed that such diffeomorphisms have a finite number of heteroclinic orbits. In addition, the classification problem of the diffeomorphisms under consideration is reduced to the problem of distinguishing orientable graphs with permutations describing the geometry of a heteroclinic intersection. However, such graphs generally do not admit polynomial distinguishing algorithms. This article proposes a new approach to the classification of cascade data. For this, each diffeomorphism f under consideration is assigned a graph whose embeddability in the ambient surface makes it possible to construct an effective algorithm for distinguishing such graphs.