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