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Isochronous systems and their quantization
F. Calogeroab a INFN — National Institute of Nuclear Physics
b University of Rome "La Sapienza"
Abstract:
We review recent results about classical isochronous systems
characterized by the presence of an open (hence fully
dimensional) region in their phase space in which all their
solutions are completely periodic (i.e., periodic in all
degrees of freedom) with the same fixed period
(independent of the initial data provided they are inside
the isochronicity region). We report a technique for generating
such systems, whose wide applicability justifies the statement that
isochronous systems are not rare. We also present an analogous
technique applicable to a vast class of Hamiltonian systems and
generating isochronous Hamiltonian systems. We also report some
results concerning the quantized versions of such systems.
Keywords:
integrable system, isochronous system, quantization.
Citation:
F. Calogero, “Isochronous systems and their quantization”, TMF, 152:1 (2007), 5–19; Theoret. and Math. Phys., 152:1 (2007), 882–893
Linking options:
https://www.mathnet.ru/eng/tmf6066https://doi.org/10.4213/tmf6066 https://www.mathnet.ru/eng/tmf/v152/i1/p5
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