Stability domain of planar symplectic maps using invariant manifolds.

0 The Symplectic Sum Formula for Gromov - Witten Invariants

In the symplectic category there is a ‘connect sum’ operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds. This paper establishes a formula for the Gromov-Witten invariants of a symplectic sum Z = X#Y in terms of the relative GW invariants ofX and Y . Several applications to enumerative geometry are given. Gromov-Witten invariants are co...

Invariant curves near Hamiltonian Hopf bifurcations of D symplectic maps

In this paper we give a numerical description of the neighbourhood of a xed point of a symplectic map undergoing a transition from linear stability to complex instability i e the so called Hamiltonian Hopf bifurcation We have considered both the direct and inverse cases The study is based on the numerical computation of the Lyapunov families of invariant curves near the xed point We show how th...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Complete Invariants for Hamiltonian Torus Actions with Two Dimensional Quotients

We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces.

Tall Complexity One Hamiltonian Torus Actions

We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces.