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Summer 2010 Cohomology of decomposition and the multiplicity theorem with applications to dynamical systems
Leon A. Luxemburg
Illinois J. Math. 54(2): 485-499 (Summer 2010). DOI: 10.1215/ijm/1318598669

Abstract

The article obtains some lower bounds for the sectional category of a map based on the cohomology of the base space and the total space. We also obtain geometric results on the multiplicity of maps and show applications to equilibria on the boundary of stability regions (basins of attraction) of dynamical systems on differentiable manifolds. We consider a number of generalizations of Lusternik–Schnirelmann’s theorem which states that if a covering of an $n$ dimensional sphere consists of $n + 1$ closed sets, then at least one of the sets contains antipodal points. An elementary proof is given for a generalization of this result to packings of Euclidean spaces.

Citation

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Leon A. Luxemburg. "Cohomology of decomposition and the multiplicity theorem with applications to dynamical systems." Illinois J. Math. 54 (2) 485 - 499, Summer 2010. https://doi.org/10.1215/ijm/1318598669

Information

Published: Summer 2010
First available in Project Euclid: 14 October 2011

zbMATH: 1246.55002
MathSciNet: MR2846470
Digital Object Identifier: 10.1215/ijm/1318598669

Subjects:
Primary: 55M30
Secondary: 37D15, 55R10

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign

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Vol.54 • No. 2 • Summer 2010
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