35 citations · 421 across the 77 of their papers we have counts for
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Non-adiabatic holonomy operators in classical and quantum completely integrable systems
G. Giachetta, L. Mangiarotti, G. Sardanashvily
Given a completely integrable system, we associate to any connection on its invariant tori fibred over a parameter manifold the classical and quantum holonomy operator (generalized…
A note on the KAM theorem for partially integrable Hamiltonian systems
G. Giachetta, L. Mangiarotti, G. Sardanashvily
We provide a symplectic reduction of a partially integrable Hamiltonian system to a completely integrable one. The KAM theorem is applied to this reduced completely integrable Hami…
Recursion operators between degenerate Poisson structures
G. Sardanashvily
Two degenerate Poisson structures of the same rank possess a recursion operator if and only if their characteristic distributions coincide.
Bi-Hamiltonian partially integrable systems
G. Giachetta, L. Mangiarotti, G. Sardanashvily
Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open n…
The Liouville-Arnold-Nekhoroshev theorem for non-compact invariant manifolds
E. Fiorani, G. Giachetta, G. Sardanashvily
Under ceratin conditions, generalized action-angle coordinates can be introduced near non-compact invariant manifolds of completely and partially integrable Hamiltonian systems.
The bracket and the evolution operator in covariant Hamiltonian field theory
G. Sardanashvily
No bracket determines the evolution operator in covariant (polysymplectic and multisymplectic) Hamiltonian field theory.