Séance du vendredi 1er Juin 2012

Lieu : IHP, Salle 201.

- 11:00 Clémence Labrousse (IMJ) :
Complexity of geodesic flows on tori.

- 14:00 Frol Zapolsky (LMU München)
Geometry of contactomorphism groups, contact rigidity, and dynamics.

- 16:00 Mikhail Khanevsky (IAS)
Hofer's metric and disk translations on an annulus

Résumés des exposés du 1er juin :

11:00  Clémence Labrousse (IMJ)  Complexity of geodesic flows on tori.

We look for the metrics on tori that minimize the entropy of the associated geodesic flow. Since the topological entropy may vanish, we study the polynomial entropy. We first see that flat metrics on $\T^n$ are minimizers for the polynomial entropy. Then we see that among a particular class of integrable geodesic flow on the torus $\T^2$, the flat metrics are strict local minimizers for the polynomial entropy.

14:00 Frol Zapolsky (LMU München)

Title: Geometry of contactomorphism groups, contact rigidity, and dynamics.

Abstract: "I'll use spectral invariants for Legendrians in jet spaces (1) to establish the existence of a biinvariant partial order and a biinvariant integer-valued metric on the contactomorphism group of T^*N \times S^1; (2) to prove some forms of contact rigidity, namely that certain subsets of T^*N \times S^1 can't be disjoined from the zero section by a contact isotopy; and (3) to prove some multiplicity results on orbits of contact flows with Legendrian boundary conditions."

16:00 Mikhail Khanevsky (IAS)

Title: Hofer's metric and disk translations on an annulus

Abstract: Denote the annulus M=(0,1)\times S^1 and consider Hamiltonians that translate various subsets of M along the S^1 coordinate.
Translation of a smaller annulus A=[a,b]\times S^1 requires
Hofer's energy of at least n\times Area(A) where n denotes
the translation number. On the other hand, a displaceable disk
can be translated arbitrarily far using a bounded amount of energy.
In the talk we will consider the case of a non-displaceable disk D.
We show that the necessary energy grows linearly with translation number,
but the growth rate is lower than Area(D).
This way, a non-displaceable disk can be seen as an "intermediate" case
between the annulus A and a displaceable disk.