Poincaré-Bendixson theory for leaves of codimension one
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- by John Cantwell and Lawrence Conlon PDF
- Trans. Amer. Math. Soc. 265 (1981), 181-209 Request permission
Abstract:
The level of a local minimal set of a ${C^2}$ codimension-one foliation of a compact manifold is a nonnegative integer defined inductively, level zero corresponding to the minimal sets in the usual sense. Each leaf of a local minimal set at level $k$ is at level $k$. The authors develop a theory of local minimal sets, level, and how leaves at level $k$ asymptotically approach leaves at lower level. This last generalizes the classical Poincaré-Bendixson theorem and provides information relating growth, topological type, and level, e.g. if $L$ is a totally proper leaf at level $k$ then $L$ has exactly polynomial growth of degree $k$ and topological type $k - 1$.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 265 (1981), 181-209
- MSC: Primary 57R30; Secondary 58F18
- DOI: https://doi.org/10.1090/S0002-9947-1981-0607116-8
- MathSciNet review: 607116