Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Proceedings of the Workshop on  Geometric Aspects of Integrable Systems  (July 17−19, 2006, University of Coimbra, Portugal)

The Guest Editors for this special issue are Francesco Calogero (Univ. Roma, La Sapienza), Jean-Pierre Françoise (Univ. Pierre et Marie Curie, Paris 6), Juan Carlos Marrero (Univ. La Laguna), Nenad Manojlovic (Univ. Algarve) and Joana Nunes da Costa (Univ. Coimbra).

The workshop Geometric Aspects of Integrable Systems was held from July 17-19, 2006 at the Mathematics Department of the University of Coimbra, Portugal, as a satellite workshop of the International Congress of Mathematicians, Madrid 2006. The workshop attracted more than forty participants from all over the world and the focus was on the following topics: Hamiltonian integrable systems, bi-Hamiltonian systems and Poisson geometry, quantum integrable systems, superintegrability, separability, reduction and Lie algebroids in mechanics.

Eight plenary lectures were presented in the mornings by invited speakers: Francesco Calogero, José Cariñena, Pantelis Damianou, Jean-Pierre Françoise, Franco Magri, Juan Carlos Marrero, Yavuz Nutku and Orlando Ragnisco. The programme also included twenty-five contributions from other participants delivered in two parallel sessions in the afternoons.

Professor Franco Magri and the guest editors of this special issue of SIGMA constituted the scientific committee of the workshop and the local organizing committee included Raquel Caseiro, Nenad Manojlović, Joana Nunes da Costa, Joana Teles Correia and Patrícia Santos.

We gratefully acknowledge the financial support provided by the Centre for Mathematics of the University of Coimbra, by the project Group Theoretical Methods in Integrable Systems, POCI/MAT/58452/2004, by the Department of Mathematics of the University of Coimbra and by the Foundation for Science and Technology. We wish to express our gratitude to Paulo Antunes and Margarida Camarinha for their support. Finally, we would like to thank all the participants for creating an excellent atmosphere at the workshop, and especially the contributors to this volume.

March 23, 2007             The Guest Editors         

Papers in this Issue:

Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System
Francesco Fassò and Andrea Giacobbe
SIGMA 3 (2007), 051, 12 pages   [ abs   pdf   ps ]
Lie Algebroids in Classical Mechanics and Optimal Control
Eduardo Martínez
SIGMA 3 (2007), 050, 17 pages   [ abs   pdf   ps ]
Reduction of Symplectic Lie Algebroids by a Lie Subalgebroid and a Symmetry Lie Group
David Iglesias, Juan Carlos Marrero, David Martín de Diego, Eduardo Martínez and Edith Padrón
SIGMA 3 (2007), 049, 28 pages   [ abs   pdf   ps ]
Some Remarks on the KP System of the Camassa-Holm Hierarchy
Giovanni Ortenzi
SIGMA 3 (2007), 047, 10 pages   [ abs   pdf   ps ]
A Journey Between Two Curves
Sergey A. Cherkis
SIGMA 3 (2007), 043,  9 pages   [ abs   pdf   ps ]
An Explicit Formula for Symmetric Polynomials Related to the Eigenfunctions of Calogero-Sutherland Models
Martin Hallnäs
SIGMA 3 (2007), 037, 17 pages   [ abs   pdf   ps ]
By Magri's Theorem, Self-Dual Gravity is Completely Integrable
Yavuz Nutku
SIGMA 3 (2007), 034,  6 pages   [ abs   pdf   ps ]
Continuous and Discrete (Classical) Heisenberg Spin Chain Revised
Orlando Ragnisco and Federico Zullo
SIGMA 3 (2007), 033,  6 pages   [ abs   pdf   ps ]
A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog
José F. Cariñena, Manuel F. Rañada and Mariano Santander
SIGMA 3 (2007), 030, 23 pages   [ abs   pdf   ps ]
Deformation Quantization in White Noise Analysis
Rémi Léandre
SIGMA 3 (2007), 027,  8 pages   [ abs   pdf   ps ]
A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold
Willy Sarlet
SIGMA 3 (2007), 024,  9 pages   [ abs   pdf   ps ]
Construction of the Bethe State for the Eτ,η(so3) Elliptic Quantum Group
Nenad Manojlović and Zoltán Nagy
SIGMA 3 (2007), 004, 10 pages   [ abs   pdf   ps ]
Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials
A. Enciso, F. Finkel, A. González-López and M.A. Rodríguez
SIGMA 2 (2006), 073, 11 pages   [ abs   pdf   ps ]

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