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Qualitative Properties of Foliations on Closed Surfaces

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Abstract

The paper contains a survey of the author's results obtained at last ten years on a research of foliations with singularities on closed surfaces. The following problems of the qualitative theory of foliations are considered.

(1) Generalization of the Poincaré–Bendixon theory.

(2) Kneser problem and estimation of the number of quasiminimal sets.

(3) Anosov problem about interrelation between geodesics and asymptotic behavior of leaves of foliations.

(4) Topological classification of supertransitive foliations.

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  1. Niznii Novgorod State Technical University, Niznii Novgorod, Russia

    S. Kh. Aranson

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Aranson, S.K. Qualitative Properties of Foliations on Closed Surfaces. Journal of Dynamical and Control Systems 6, 127–157 (2000). https://doi.org/10.1023/A:1009525823422

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