Rotation of accessible points in essential annular continua

Jeudi 2 mars 2017 14:00-15:00 - Luis Hernandez Corbato - ICMAT, Madrid

Résumé : The notion of rotation number, which goes back to Poincaré, has been generalized to several settings, for example annuli or tori. Unlike in S^1, different orbits may present different rotation numbers. A paradigmatic example is Birkhoff attractor C in the annulus, C contains periodic points of rotation number equal to any rational number in a non—trivial interval. We focus in the set of points p of C which are accessible from above, i.e., there is a path contained in the upper region of the complement of C that lands at p. This set has a natural circular order and thus a rotation number \widehat{\rho} that turns out to be an endpoint of the rotation interval of C. In the talk we will give a result that connects \widehat{\rho} to the rotation number of the forward or backward orbit of any accessible point. The result is valid for any invariant essential annular continua.

Lieu : Bâtiment 425, salle 121-123

Notes de dernières minutes : Café culturel assuré à 13h par Sylvain Crovisier.

Rotation of accessible points in essential annular continua  Version PDF