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Integrable Hamiltonian Systems - Geometry, Topology, Classification (Paperback)
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Integrable Hamiltonian Systems - Geometry, Topology, Classification (Paperback)
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Integrable Hamiltonian systems have been of growing interest over
the past 30 years and represent one of the most intriguing and
mysterious classes of dynamical systems. This book explores the
topology of integrable systems and the general theory underlying
their qualitative properties, singularites, and topological
invariants. The authors, both of whom have contributed
significantly to the field, develop the classification theory for
integrable systems with two degrees of freedom. This theory allows
one to distinguish such systems up to two natural equivalence
relations: the equivalence of the associated foliation into
Liouville tori and the usual orbital equaivalence. The authors show
that in both cases, one can find complete sets of invariants that
give the solution of the classification problem. The first part of
the book systematically presents the general construction of these
invariants, including many examples and applications. In the second
part, the authors apply the general methods of the classification
theory to the classical integrable problems in rigid body dynamics
and describe their topological portraits, bifurcations of Liouville
tori, and local and global topological invariants. They show how
the classification theory helps find hidden isomorphisms between
integrable systems and present as an example their proof that two
famous systems--the Euler case in rigid body dynamics and the
Jacobi problem of geodesics on the ellipsoid--are orbitally
equivalent. Integrable Hamiltonian Systems: Geometry, Topology,
Classification offers a unique opportunity to explore important,
previously unpublished results and acquire generally applicable
techniques and tools that enable you to work with a broad class of
integrable systems.
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