From Brouwer theory to the study of homeomorphisms of surfaces

• Autores: Patrice Le Calvez
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé, Javier Soria de Diego, Juan Luis Varona Malumbres, Joan Verdera, Vol. 3, 2006, ISBN 978-3-03719-022-7, págs. 77-98
• Idioma: inglés
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• Resumen

  • We will state an equivariant foliated version of the classical Brouwer PlaneTranslation Theorem and will explain how to apply this result to the study of homeomorphisms of surfaces.

    In particular we will explain why a diffeomorphism of a closed oriented surface of genus . 1 that is the time-one map of a time dependent Hamiltonian vector field has infinitely many periodic orbits. This gives a positive answer in the case of surfaces to a more general question stated by C. Conley. We will give a survey of some recent results on homeomorphisms and diffeomorphisms of surfaces and will explain the links with the improved version of Brouwer�fs theorem.