Abstract: The level of a local minimal set of a C2 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 Poincare-Bendixson theorem and provides information relating growth, topological type, and level, e.g. if L is a totally pr...
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Topics: 
Pure mathematics
Combinatorics
Discrete mathematics