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Structure-Preserving Reduced Basis Methods For Poisson Systems

Publications associées (41)

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Analysis of adiabatic trapping for quasi-integrable area-preserving maps

Cedric Jean-François Hernalsteens, Massimo Giovannozzi

Trapping phenomena involving nonlinear resonances have been considered in the past in the framework of adiabatic theory. Several results are known for continuous-time dynamical systems generated by Hamiltonian flows in which the combined effect of nonlinea ...

American Physical Society2014

Extensions of Lie-Rinehart algebras and cotangent bundle reduction

Tudor Ratiu

Let Q denote a smooth manifold acted upon smoothly by a Lie group G. The G-action lifts to an action on the total space TQ of the cotangent bundle of Q and hence on the standard symplectic Poisson algebra of smooth functions on TQ. The Poisson algebra of ...

Oxford University Press2013

New Techniques For Obtaining Schubert-Type Formulas For Hamiltonian Manifolds

Silvia Sabatini

In [GT], Goldin and Tolman extend some ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. (See also [Kn99,Kn08].) The main goal of this paper is to build on this ...

Int Press Boston, Inc2013

A class of Neumann type systems and its application

Jinbing Chen

A class of Neumann type systems are derived separating the spatial and temporal variables for the 2+1 dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation and the modified Korteweg-de Vries (mKdV) hierarchy. The Lax-Moser matrix of Neumann type s ...

International Press2012

Transport, Flux And Growth Of Homoclinic Floer Homology

We point out an interesting relation between transport in Hamiltonian dynamics and Floer homology. We generalize homoclinic Floer homology from R-2 and closed surfaces to two-dimensional cylinders. The relative symplectic action of two homoclinic points is ...

Amer Inst Mathematical Sciences2012

Geometry of nonabelian charged fluids

Tudor Ratiu, François Gay-Balmaz

The goal of this paper is to derive the Hamiltonian structure of polarized and magnetized Euler-Maxwell fluids by reduction of the canonical symplectic form on phase space, and to generalize the dynamics to the nonabelian case. The Hamiltonian function we ...

2011

Flexible beam in R3 under large overall motions and Asynchronous Variational Integrators

Yves Weinand, Tudor Ratiu, François Gay-Balmaz, François Marie Alain Demoures

The theory of discrete variational mechanics has its roots in the optimal control literature of the 1960's. The past ten years have seen a major development of discrete variational mechanics and corresponding numerical integrators, due largely to pioneerin ...

IABSE ETH Zurich2011

Higher order Lagrange-Poincar, and Hamilton-Poincar, reductions

Tudor Ratiu, François Gay-Balmaz

Motivated by the problem of longitudinal data assimilation, e.g., in the registration of a sequence of images, we develop the higher-order framework for Lagrangian and Hamiltonian reduction by symmetry in geometric mechanics. In particular, we obtain the r ...

2011

A Global Version Of The Darboux Theorem With Optimal Regularity And Dirichlet Condition

Bernard Dacorogna, Olivier Kneuss

Let n > 2 be even; r >= 1 be an integer; 0 < alpha < 1; Omega be a bounded, connected, smooth, open set in R-n; and nu be its exterior unit normal. Let f, g is an element of C-r,C-alpha((Omega) over bar; Lambda(2)) be two symplectic forms (i.e., closed and ...

2011

Dirac Lie Groups, Dirac Homogeneous Spaces and the Theorem of Drinfeld

Madeleine Jotz

The notions of Poisson Lie group and Poisson homogeneous space are extended to the Dirac category. The theorem of Drinfeld on the one-to-one correspondence between Poisson homogeneous spaces of a Poisson Lie group and a special class of Lagrangian subalgeb ...

2011