Download E-books Integrable Hamiltonian Systems: Geometry, Topology, Classification PDF

By A.V. Bolsinov

Integrable Hamiltonian platforms were of transforming into curiosity over the last 30 years and signify some of the most exciting and mysterious periods of dynamical structures. This ebook explores the topology of integrable structures and the overall thought underlying their qualitative homes, singularites, and topological invariants.

The authors, either one of whom have contributed considerably to the sphere, increase the class conception for integrable structures with levels of freedom. This concept permits one to tell apart such structures as much as traditional equivalence kin: the equivalence of the linked foliation into Liouville tori and the standard orbital equaivalence. The authors convey that during either circumstances, you will see whole units of invariants that supply the answer of the type challenge.

The first a part of the e-book systematically offers the overall building of those invariants, together with many examples and functions. within the moment half, the authors practice the overall equipment of the category idea to the classical integrable difficulties in inflexible physique dynamics and describe their topological pics, bifurcations of Liouville tori, and native and worldwide topological invariants. They express how the category concept is helping locate hidden isomorphisms among integrable structures and current for instance their evidence that recognized systems--the Euler case in inflexible physique dynamics and the Jacobi challenge of geodesics at the ellipsoid--are orbitally equivalent.

Integrable Hamiltonian structures: Geometry, Topology, category bargains a special chance to discover vital, formerly unpublished effects and obtain usually appropriate innovations and instruments that show you how to paintings with a vast category of integrable platforms.

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