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The necessity of the star-shaped condition on Ding's version of the Poincaré-Birkhoff theorem

TítuloThe necessity of the star-shaped condition on Ding's version of the Poincaré-Birkhoff theorem
Publication TypeUnpublished
Year of Publication2006
AuthorsMartins R, Ureña AJ
Series TitlePreprint
AbstractW-Y. Ding proved a generalization of the Poincaré-Birkhoff fixed point theorem not requiring that the boundary curves of the anular region be circles and invariant. However the inner boundary is required to be star-shaped with respect to the origin. We construct a counterexample that shows that the star-shaped condition is necessary.
URLhttp://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2006/16_06.pdf