Some remarks on the Poincaré-Birkhoff theorem
By P. Calvez, Jian Wang. 2009
46 citations recorded by the source corpus.
We define the notion of a positive path of a homeomorphism of a topological space. It seems to be a natural object to understand Birkhoff's arguments in his proof of the celebrated Poincare-Birkhoff theorem. We write the proof of this theorem, by using positive paths, and the proof of its generalization due to P. Carter. We will also explain the links with the free disk chains introduced in the subject by J. Franks. We will finish the paper by studying the local versions where the upper curve is not invariant and will explain why this curve or its image must be a graph to get such a generalization.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/3a83659967251df1f70f65156d8a6d4ef3b326d1
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In Geometry and Topology
Citations in the corpus
- Periodic solutions of perturbed Hamiltonian systems in the plane by the use of the Poincaré-Birkhoff theorem (2012, background): “Wang in [51] provided an example showing that a star-shapedness assumption on the outer boundary is also needed.”