F Nous contacter


0

Documents  37C10 | enregistrements trouvés : 2

O
     

-A +A

Sélection courante (0) : Tout sélectionner / Tout déselectionner

P Q

Post-edited  Which geodesic flows are left-handed?
Dehornoy, Pierre (Auteur de la Conférence) | CIRM (Editeur )

Left-handed flows are 3-dimensional flows which have a particular topological property, namely that every pair of periodic orbits is negatively linked. This property (introduced by Ghys in 2007) implies the existence of as many Bikrhoff sections as possible, and therefore allows to reduce the flow to a suspension in many different ways. It then becomes natural to look for examples. A construction of Birkhoff (1917) suggests that geodesic flows are good candidates. In this conference we determine on which hyperbolic orbifolds is the geodesic flow left-handed: the answer is that yes if the surface is a sphere with three cone points, and no otherwise.
dynamical system - geodesic flow - knot - periodic orbit - global section - linking number - fibered knot
Left-handed flows are 3-dimensional flows which have a particular topological property, namely that every pair of periodic orbits is negatively linked. This property (introduced by Ghys in 2007) implies the existence of as many Bikrhoff sections as possible, and therefore allows to reduce the flow to a suspension in many different ways. It then becomes natural to look for examples. A construction of Birkhoff (1917) suggests that geodesic flows ...

37C27 ; 37C15 ; 37C10 ; 57M25

The notion of singular hyperbolicity for vector fields has been introduced by Morales, Pacifico and Pujals in order to extend the classical uniform hyperbolicity and include the presence of singularities. This covers the Lorenz attractor. I will present a joint work with Dawei Yang which proves a dichotomy in the space of three-dimensional $C^{1}$-vector fields, conjectured by J. Palis: every three-dimensional vector field can be $C^{1}$-approximated by one which is singular hyperbolic or by one which exhibits a homoclinic tangency. The notion of singular hyperbolicity for vector fields has been introduced by Morales, Pacifico and Pujals in order to extend the classical uniform hyperbolicity and include the presence of singularities. This covers the Lorenz attractor. I will present a joint work with Dawei Yang which proves a dichotomy in the space of three-dimensional $C^{1}$-vector fields, conjectured by J. Palis: every three-dimensional vector field can be $C^{1}...

37C29 ; 37Dxx ; 37C10 ; 37F15

Nuage de mots clefs ici

Z