Аннотация:
Bifibrations, in symplectic geometry called also dual pairs, play a relevant role in the theory of superintegrable
Hamiltonian systems. We prove the existence of an analogous bifibrated geometry in dynamical systems with a symmetry group such that the reduced dynamics is periodic. The integrability of such systems has been proven by M. Field and J. Hermans with a reconstruction technique. We apply the result to the nonholonomic system of a ball rolling on a surface of revolution.
Ключевые слова:
systems with symmetry; reconstruction; integrable systems; nonholonomic systems.
Поступила:20 ноября 2006 г.; в окончательном варианте 15 марта 2007 г.; опубликована 22 марта 2007 г.
Образец цитирования:
Francesco Fassò, Andrea Giacobbe, “Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic
System”, SIGMA, 3 (2007), 051, 12 pp.
\RBibitem{FasGia07}
\by Francesco Fass\`o, Andrea Giacobbe
\paper Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a~Nonholonomic
System
\jour SIGMA
\yr 2007
\vol 3
\papernumber 051
\totalpages 12
\mathnet{http://mi.mathnet.ru/sigma177}
\crossref{https://doi.org/10.3842/SIGMA.2007.051}
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Цитирование в формате AMSBIB
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