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Books > Reference & Interdisciplinary > Communication studies > Information theory > Cybernetics & systems theory
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Hamiltonian Systems with Three or More Degrees of Freedom (Hardcover, 1999 ed.)
Loot Price: R8,684
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Hamiltonian Systems with Three or More Degrees of Freedom (Hardcover, 1999 ed.)
Series: NATO Science Series C, 533
Expected to ship within 10 - 15 working days
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A survey of current knowledge about Hamiltonian systems with three
or more degrees of freedom and related topics. The Hamiltonian
systems appearing in most of the applications are non-integrable.
Hence methods to prove non-integrability results are presented and
the different meaning attributed to non-integrability are
discussed. For systems near an integrable one, it can be shown
that, under suitable conditions, some parts of the integrable
structure, most of the invariant tori, survive. Many of the papers
discuss near-integrable systems. From a topological point of view,
some singularities must appear in different problems, either
caustics, geodesics, moving wavefronts, etc. This is also related
to singularities in the projections of invariant objects, and can
be used as a signature of these objects. Hyperbolic dynamics appear
as a source on unpredictable behaviour and several mechanisms of
hyperbolicity are presented. The destruction of tori leads to
Aubrey-Mather objects, and this is touched on for a related class
of systems. Examples without periodic orbits are constructed,
against a classical conjecture. Other topics concern higher
dimensional systems, either finite (networks and localised
vibrations on them) or infinite, like the quasiperiodic SchrAdinger
operator or nonlinear hyperbolic PDE displaying quasiperiodic
solutions. Most of the applications presented concern celestial
mechanics problems, like the asteroid problem, the design of
spacecraft orbits, and methods to compute periodic solutions.
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