Special Year 2011-12: Workshop on Symplectic Dynamics

This talk will discuss joint work with Michael Handel concerning the dynamic structure of symplectic diffeomorphisms of the two-sphere. The intended application is the study of groups of "fully supported" diffeomorphisms (e.g. analytic) and the...

Geodesic flows of Riemannian or Finsler manifolds have been the only known contact Anosov flows. We show that even in dimension 3 the world of contact Anosov flow is vastly larger via a surgery construction near a transverse Legendrian knot that...

We prove that there is an open and dense set in the C2 topology of riemannian metrics on the 2-sphere whose geodesic flow has an elliptic closed geodesic.

This result recovers, in a generic sense, a theorem by H. Poincaré 1904 and proves a conjecture...

Newton's differential equations for the N-body problem have rotational and translational symmetry. Their flow is incomplete due to collisions. Symplectic reduction eliminates the symmetries. Levi-Civita regularization eliminates the binary collision...

I will describe an example of a $C^\infty$ volume preserving topologically transitive diffeomorphism of a compact smooth Riemannian manifold which is ergodic (indeed is Bernoulli) on an open and dense subset $U$ of not full measure and has zero...

Let $\phi : \mathbb R\times X\to X$ be a dynamical system, an $\mathbb R$-action, defined on the metric space $X$. A nonempty, closed invariant set is minimal if it contains no proper, nonempty, closed invariant subset. We will show a construction...

In this talk we study the existence question of disk-like global surfaces of section of tight Reeb flows on the 3-sphere and on lens spaces, and describe some applications. For instance, we find new global sections on strictly convex 3-dimensional...

Introduced by R. Schwartz about 20 years ago, the pentagram map acts on plane n-gons, considered up to projective equivalence, by drawing the diagonals that connect second-nearest vertices and taking the new n-gon formed by their intersections. The...

We will explore some connections between Hamiltonian dynamics and the geometry of symplectic manifolds. We show some intersection properties between isotropic and coisotropic submanifolds, with applications to hoteroclinic connections in Hamiltonian...

We prove that an elliptic equilibrium point with Diophantine frequencies for an analytic Hamiltonian system is always accumulated by invariant Lagnrangian tori. Generically the set of such tori has positive measure, but if this is always the case is...