Integrable Hamiltonian Systems: Geometry, Topology, by A.V. Bolsinov,A.T. Fomenko

Integrable Hamiltonian platforms were of growing to be curiosity over the last 30 years and signify some of the most interesting and mysterious sessions of dynamical structures. This booklet explores the topology of integrable structures and the overall thought underlying their qualitative houses, singularites, and topological invariants.

The authors, either one of whom have contributed considerably to the sector, improve the category idea for integrable platforms with levels of freedom. This concept permits one to differentiate such platforms as much as average equivalence kinfolk: the equivalence of the linked foliation into Liouville tori and the standard orbital equaivalence. The authors express that during either situations, you can see entire units of invariants that supply the answer of the type challenge.

The first a part of the e-book systematically provides the overall building of those invariants, together with many examples and functions. within the moment half, the authors practice the overall tools of the type conception 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 exhibit how the class concept is helping locate hidden isomorphisms among integrable structures and current as an instance their facts that recognized systems--the Euler case in inflexible physique dynamics and the Jacobi challenge of geodesics at the ellipsoid--are orbitally equivalent.

Integrable Hamiltonian platforms: Geometry, Topology, class bargains a distinct chance to discover vital, formerly unpublished effects and obtain more often than not acceptable options and instruments that assist you to paintings with a extensive category of integrable systems.