0000000000798103
AUTHOR
Maxime Lagrange
Braiding minimal sets of vector fields
We extend a classical but fundamental theorem of knot and braid theories to describe the geometry of nonsingular minimal sets of 3-dimensional flows.
Topological lower bounds on the distance between area preserving diffeomorphisms
Area preserving diffeomorphisms of the 2-disk which are Identity near the boundary form a group which can be equipped, using theL2-norm on its Lie algebra, with a right invariant metric. In this paper we give a lower bound on the distance between diffeomorphisms which is invariant under area preserving changes of coordinates and which improves the lower bound induced by the Calabi invariant. In the case of renormalizable and infinitely renormalizable maps, our estimate can be improved and computed.