Zobrazeno 1 - 10
of 50
pro vyhledávání: '"Degiovanni, Luca"'
It is natural to investigate if the quantization of an integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of motion quadrat
Externí odkaz:
http://arxiv.org/abs/1608.07243
Publikováno v:
SIGMA 11 (2015), 094, 9 pages
The coupling-constant metamorphosis is applied to modified extended Hamiltonians and sufficient conditions are found in order that the transformed high-degree first integral of the transformed Hamiltonian is determined by the same algorithm which com
Externí odkaz:
http://arxiv.org/abs/1509.07288
We generalize the idea of "extension of Hamiltonian systems" -- developed in a series of previous articles -- which allows the explicit construction of Hamiltonian systems with additional non-trivial polynomial first integrals of arbitrarily high deg
Externí odkaz:
http://arxiv.org/abs/1404.4825
The technique of "extension" allows to build $(n+1)$-dimensional Hamiltonian systems with a non-trivial polynomial in the momenta first integral of any given degree starting from a $n$-dimensional Hamiltonian satisfying some additional properties. Un
Externí odkaz:
http://arxiv.org/abs/1310.5690
Publikováno v:
SIGMA 8 (2012), 070, 12 pages
A procedure to extend a superintegrable system into a new superintegrable one is systematically tested for the known systems on $\mathbb E^2$ and $\mathbb S^2$ and for a family of systems defined on constant curvature manifolds. The procedure results
Externí odkaz:
http://arxiv.org/abs/1210.3126
Publikováno v:
J. Phys.: Conf. Ser. 343 012101 (2012) (v1 version)
In previous papers we determined necessary and sufficient conditions for the existence of a class of natural Hamiltonians with non-trivial first integrals of arbitrarily high degree in the momenta. Such Hamiltonians were characterized as (n+1)-dimens
Externí odkaz:
http://arxiv.org/abs/1111.0030
Publikováno v:
SIGMA 7 (2011), 038, 12 pages
We describe a procedure to construct polynomial in the momenta first integrals of arbitrarily high degree for natural Hamiltonians $H$ obtained as one-dimensional extensions of natural (geodesic) $n$-dimensional Hamiltonians $L$. The Liouville integr
Externí odkaz:
http://arxiv.org/abs/1101.5975
We give an explicit and concise formula for higher-degree polynomial first integrals of a family of Calogero-type Hamiltonian systems in dimension three. These first integrals, together with the already known ones, prove the maximal superintegrabilit
Externí odkaz:
http://arxiv.org/abs/1002.2735
Superintegrable Hamiltonian systems describing the interactions among three point masses on a line have been described in [2]. Here, we show examples of how the approach of above can be extended to a higher number of particles on a line and on higher
Externí odkaz:
http://arxiv.org/abs/0907.5288
We consider classical three-body interactions on a Euclidean line depending on the reciprocal distance of the particles and admitting four functionally independent quadratic in the momenta first integrals. These systems are superseparable (i.e. multi
Externí odkaz:
http://arxiv.org/abs/0802.1353