Invariant incompatible Poisson structures

1995 ◽  
Vol 450 (1940) ◽  
pp. 723-730 ◽  
Keyword(s):  
Hamiltonian System ◽  
Poisson Structure ◽  
Integrable Hamiltonian System ◽  
Complete Classification ◽  
Degenerate Case ◽  
Poisson Structures ◽  
Completely Integrable ◽  
Completely Integrable Hamiltonian System ◽  
Invariant Submanifolds

Supplemental invariant Poisson structures P c which are incompatible with the original Poisson structure P 1 are discovered for an arbitrary completely integrable Hamiltonian system. For the non-degenerate case, the complete classification of the invariant Poisson structures P c is obtained provided that the invariant submanifolds of the integrable Hamiltonian system are compact. The instability of the property of compatibility of any supplemental invariant non-degenerate Poisson structure P 2 with P 1 is established.

COMPLETELY AND PARTIALLY INTEGRABLE HAMILTONIAN SYSTEMS IN THE NONCOMPACT CASE

2004 ◽  
Vol 01 (03) ◽  
pp. 167-183 ◽  
Author(s):  
EMANUELE FIORANI
Keyword(s):  
Hamiltonian System ◽  
Hamiltonian Systems ◽  
Integrable Hamiltonian System ◽  
Time Dependent ◽  
Integrable Hamiltonian Systems ◽  
Invariant Submanifold ◽  
Completely Integrable ◽  
Completely Integrable Hamiltonian System

Action-angle coordinates are shown to exist around an instantly compact invariant submanifold of a time-dependent completely integrable Hamiltonian system. Partially integrable Hamiltonian systems are also considered in the noncompact case; a comparison is made with other possible approaches. Results on symplectically complete foliations contained in the Appendix A can be used to give alternative proofs of some propositions.

A completely integrable Hamiltonian system

1996 ◽  
Vol 37 (6) ◽  
pp. 2863-2871 ◽  
Author(s):  
F. Calogero ◽  
J.‐P. Françoise
Keyword(s):  
Hamiltonian System ◽  
Integrable Hamiltonian System ◽  
Completely Integrable ◽  
Completely Integrable Hamiltonian System

scholarly journals Isomonodromic deformation of Fuchsian projective connections on elliptic curves

2003 ◽  
Vol 171 ◽  
pp. 127-161 ◽  
Author(s):  
Shingo Kawai
Keyword(s):  
Hamiltonian System ◽  
Differential Equations ◽  
Elliptic Curves ◽  
Integrable Hamiltonian System ◽  
Second Order ◽  
Isomonodromic Deformation ◽  
Isomonodromic Deformations ◽  
Completely Integrable ◽  
Completely Integrable Hamiltonian System ◽  
Fuchsian Differential Equations

AbstractWe consider isomonodromic deformations of second-order Fuchsian differential equations on elliptic curves. The isomonodromic deformations are described as a completely integrable Hamiltonian system.

scholarly journals DONAGI–MARKMAN CUBIC FOR THE GENERALIZED HITCHIN SYSTEM

2014 ◽  
Vol 25 (02) ◽  
pp. 1450016 ◽  
Author(s):  
UGO BRUZZO ◽  
PETER DALAKOV
Keyword(s):  
Hamiltonian System ◽  
Cotangent Bundle ◽  
Integrable Hamiltonian System ◽  
Maximal Rank ◽  
Symmetric Power ◽  
Period Map ◽  
The Third ◽  
Hitchin System ◽  
Completely Integrable Hamiltonian System ◽  
Symplectic Leaves

Donagi and Markman (1993) have shown that the infinitesimal period map for an algebraic completely integrable Hamiltonian system (ACIHS) is encoded in a section of the third symmetric power of the cotangent bundle to the base of the system. For the ordinary Hitchin system the cubic is given by a formula of Balduzzi and Pantev. We show that the Balduzzi–Pantev formula holds on maximal rank symplectic leaves of the G-generalized Hitchin system.

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