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- W4287866837 abstract "Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse--Smale decomposition of a (generic) field plays a fundamental role, relating the geometric structure of phase space to a combinatorial object consisting of critical points and separatrices. Such concepts led Forman to a satisfactory theory of discrete vector fields, in close analogy to the continuous case. In this paper, we introduce discrete line fields. Again, our definition is rich enough to provide the counterparts of the basic results in the theory of continuous line fields: a Euler-Poincar'e formula, a Morse--Smale decomposition and a topologically consistent cancellation of critical elements, which allows for topological simplification of the original discrete line field." @default.
- W4287866837 created "2022-07-26" @default.
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- W4287866837 date "2020-02-18" @default.
- W4287866837 modified "2023-09-24" @default.
- W4287866837 title "Discrete Line Fields on Surfaces" @default.
- W4287866837 doi "https://doi.org/10.48550/arxiv.2002.07723" @default.
- W4287866837 hasPublicationYear "2020" @default.
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