| 概要 | Hamiltonian monodromy is the simplest obstruction to
existence of the global action variables in integrable
Haliramiltonian systems. In the simplest cases it is
related to the presence in integrable toric fibrations
of such singular fibers as pinched tori. Initially described
by Duistermaat, Nekhoroshev, Cushman in 1970-80 and
considered for a number of years as a differential geometry
curiosity, the Hamiltonian monodromy reveals recently
an interest due to its manifestation in many important
fundamental quantum problems related to simple finite
particle systems. The aim of the talk is to describe
the Hamiltonian monodromy in classical and quantum dynamical
systems with finite number of degrees of freedom and to
discuss its possible generalizations inspired by qualitative
study of real quantum physical systems. The examples: Elastic
pendulum (swing spring), hydrogen atom in fields,
rotation-vibration of triatomic molecules - will be used
to demonstrate the applications of Hamiltonian monodromy.
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