Discovery Projects - Grant ID: DP0344091

Funding Activity

Website
http://dataportal.arc.gov.au/NCGP/Web/Grant/Grant/DP0344091

Funding Status
Closed

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Funded Activity Summary

HOLOMORPHIC CURVES, REEB FLOWS AND CONTACT TOPOLOGY. Motion of a satellite is one of many examples of a Reeb dynamical system. The aim of the project is to deepen our understanding of Reeb flows. The Reeb flows, in particular, include Hamiltonian flows on three-dimensional contact type energy surfaces. To study the behaviour of Reeb flows we construct systems of global surfaces of section and study the iterates of the Poincare map, which is obtained by following the flow until it hits a surface. The main tools in constructing systems of global surfaces of section are holomorphic curves in symplectization, which are defined on punctured Riemann surfaces and solve nonlinear Cauchy-Riemann type operator. These curves are also main ingredients of new invariants of contact and symplectic manifolds. These new invariants are now known as Contact Homology and Symplectic Field Theory. In the second part of the project we develop analytical foundations for these theories.

Funded Activity Details

Start Date: 01-01-2003

End Date: 31-12-2007

Funding Scheme: Discovery Projects

Funding Amount: $185,000.00

Funder: Australian Research Council

Research Topics

ANZSRC Field of Research (FoR)

Dynamical Systems | Topology And Manifolds | Pure Mathematics |

ANZSRC Socio-Economic Objective (SEO)

Mathematical sciences

Other Keywords

Dynamical Systems | Mathematical sciences | Pure Mathematics | Topology And Manifolds

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