35 citations · 65 across the 6 of their papers we have counts for
6 papers
Lie algebras of conservation laws of variational partial differential equations
Emanuele Fiorani, Sandra Germani, Andrea Spiro
We establish a version of the first Noether Theorem, according to which the (equivalence classes of) conserved quantities of given Euler-Lagrange equations in several independent v…
Lie algebras of conservation laws of variational ordinary differential equations
Emanuele Fiorani, Andrea Spiro
We establish a new version of the first Noether Theorem, according to which the (equivalence classes of) first integrals of given Euler-Lagrange equations in one independent variab…
Geometrical aspects of integrable systems
Emanuele Fiorani
We review some basic theorems on integrability of Hamiltonian systems, namely the Liouville-Arnold theorem on complete integrability, the Nekhoroshev theorem on partial integrabili…
Noncommutative integrability on noncompact invariant manifolds
E. Fiorani, G. Sardanashvily
The Mishchenko-Fomenko theorem on noncommutative integrability of Hamiltonian systems on a symplectic manifold is extended to the case of noncompact invariant submanifolds.
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.
Geometric quantization of time-dependent completely integrable Hamiltonian systems
E. Fiorani, G. Giachetta, G. Sardanashvily
A time-dependent completely integrable Hamiltonian system is quantized with respect to time-dependent action-angle variables near an instantly compact regular invariant manifold. I…