Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Symplectic geometry.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume contains the conference proceedings of the Workshop on Global Integrability of Field Theories GIFT 2006 (Cockcroft Institute, Daresbury, UK, 11-01-06 11-03-06), which served as the final conference of the European NEST project GIFT. Within its scope, hitherto unrelated results from various domains including algebraic topology, computer algebra, differential Galois theory, integrable systems, formal theory of differential equations and physical field theories were combined.

Geometry, Algebraic --- Symplectic geometry

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Symplectic geometry --- Differential equations, Partial --- Differential equations, Partial. --- Symplectic geometry.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

In this paper the authors start with the construction of the symplectic field theory (SFT). As a general theory of symplectic invariants, SFT has been outlined in Introduction to symplectic field theory (2000), by Y. Eliashberg, A. Givental and H. Hofer who have predicted its formal properties. The actual construction of SFT is a hard analytical problem which will be overcome be means of the polyfold theory due to the present authors. The current paper addresses a significant amount of the arising issues and the general theory will be completed in part II of this paper. To illustrate the polyfold theory the authors use the results of the present paper to describe an alternative construction of the Gromov-Witten invariants for general compact symplectic manifolds.

Symplectic geometry. --- Gromov-Witten invariants.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

A wandering domain for a diffeomorphism Psi of mathbb A^n=T^*mathbb T^n is an open connected set W such that Psi ^k(W)cap W=emptyset for all kin mathbb Z^*. The authors endow mathbb A^n with its usual exact symplectic structure. An integrable diffeomorphism, i.e., the time-one map Phi ^h of a Hamiltonian h: mathbb A^no mathbb R which depends only on the action variables, has no nonempty wandering domains. The aim of this paper is to estimate the size (measure and Gromov capacity) of wandering domains in the case of an exact symplectic perturbation of Phi ^h, in the analytic or Gevrey category. Upper estimates are related to Nekhoroshev theory; lower estimates are related to examples of Arnold diffusion. This is a contribution to the "quantitative Hamiltonian perturbation theory" initiated in previous works on the optimality of long term stability estimates and diffusion times; the emphasis here is on discrete systems because this is the natural setting to study wandering domains.

Symplectic geometry. --- Symplectic groups. --- Domains of holomorphy.