Previous Conferences & Workshops

Oct
13
2011

Workshop on Symplectic Dynamics

K3 and the planar 4 body problem
Richard Montgomery
4:30pm|Wolfensohn Hall
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...
Oct
13
2011

Workshop on Symplectic Dynamics

Essential coexistence of zero and nonzero Lyapunov exponents for volume preserving maps and flows
Yakov Pesin
2:30pm|Wolfensohn Hall

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...

Oct
13
2011

Workshop on Symplectic Dynamics

Flows with nested invariant sets
Krystyna Kuperberg
11:30am|Wolfensohn Hall

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...

Oct
13
2011

Workshop on Symplectic Dynamics

Global surfaces of section of tight Reeb flows and applications
Umberto Hryniewicz
10:15am|Wolfensohn Hall
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...
Oct
13
2011

Workshop on Symplectic Dynamics

Higher pentagram maps and cluster algebras
Serge Tabachnikov
9:00am|Wolfensohn Hall
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...
Oct
12
2011

Workshop on Symplectic Dynamics

Some intersection and rigidity properties in symplectic dynamics
Jeff Xia
4:30pm|Wolfensohn Hall
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...
Oct
12
2011

Workshop on Symplectic Dynamics

KAM-Tori accumulating a Diophantine elliptic equilibrium point
Hakan Eliasson
2:30pm|Wolfensohn Hall
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...
Oct
12
2011

Workshop on Symplectic Dynamics

Regularity of weak KAM
Chong-Qing Cheng
11:30am|Wolfensohn Hall
In this talk, I will show some modulus of continuity of weak KAM solutions exhibited by Hamiltonian with multi-degrees of freedom.
Oct
12
2011

Workshop on Symplectic Dynamics

Using pseudo-holomorphic curves to approximate zero entropy Hamiltonian systems by integrable ones
Barney Bramham
10:15am|Wolfensohn Hall
Katok has asked the following informal question: In low dimensions are all conservative dynamical systems with zero topological entropy a limit of integrable systems? In this talk I will discuss an approach to this question that uses pseudo...