Objective
This project is mainly concerned with the geometry underlying integrable dynamical systems both Hamiltonian and non-hamiltonian. The best well-known examples of integrable systems are probably completely integrable Hamiltonian systems. Hamiltonian systems arise naturally in mechanical systems. For instance the motion of celestial bodies or Shrondinger equation are examples of these phenomena. Non-Hamiltonian systems arise in dynamical systems with non-holonomic constraints. Completely integrable Hamiltonian systems have their origin in Classical Mechanics but are currently present in many other disciplines like for example Algebraic Geometry (toric manifolds and mirror symmetry). A completely integrable system on a symplectic manifold is given by a moment map. Under some mild conditions, the theorem of Arnold-Liouville asserts that the regular level sets of the moment map are tori and the system on them is quasi periodic. Unfortunately this theorem does not take singularities into account.
The main goal of t his proposal is to study local and semi-local geometrical properties of integrable dynamical systems and, in particular, their normal forms in a neighbourhood of a singularity. The following objects are associated to an integrable dynamical system: a foliation, a geometrical structure on the manifold (symplectic, contact, Poisson...) and in the holonomic case also an additional geometrical structure attached to the leaves of the foliation (Lagrangian, Legendrian or isotropic). This proposal attempts to stud y normal forms a la Weinstein for general dynamical systems in symplectic, Poisson, contact and Dirac manifolds taking into account singularities. We are also interested in obtaining the equivariant version of these normal forms results. We also want to study those systems from the perspective of deformation theory and investigate the rigidity properties and infinitesimal stability properties for these systems.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics applied mathematics dynamical systems
- natural sciences mathematics pure mathematics topology symplectic topology
- natural sciences mathematics pure mathematics geometry
- natural sciences physical sciences classical mechanics
- natural sciences mathematics pure mathematics algebra algebraic geometry
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP6-2004-MOBILITY-5
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Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
TOULOUSE
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.