Very short note (7 pages) on the differential equation (1) (in
section II) plus on its discrete analogue (9) (in section III, cca
one page) describing the classical damped oscillator. The text
offers an elementary derivation of eligible Poisson brackets and a
related discussion. The most interesting part of the message appears
to concern the multi-valued nature of the Poisson structure and of
the Hamiltonian. As far as the authors (as well as the present
reviewer) know this interesting problem has not yet been discussed
in the (fairly extensive) related literature. Unfortunately, the
``publishing or perishing" authors seem to have missed the
opportunity of making their contribution longer, deeper and more
important. Having only addressed too many issues at once. Typically:
another highly interesting and closely related problem of a
consistent quantization of the system (in fact, the deep motivation
of all the similar studies) is also only covered just by a few quick
and superficial sentences.

MR2573124 Hone, A. N. W.; Senthilvelan, M. Note on the Poisson
structure of the damped oscillator. J. Math. Phys. 50 (2009), no.
10, 102902, 7 pp. 81Qxx (81Sxx)