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Small divisors with spatial structure in infinite dimensional Hamiltonian systems. (English) Zbl 0702.58065
Summary: A general perturbation theory of the Kolmogorov-Arnold-Moser type is described concerning the existence of infinite dimensional invariant tori in nearly integrable hamiltonian systems. The key idea is to consider hamiltonians with a spatial structure and to express all quantitative aspects of the theory in terms of rather general weight functions on such structures. This approach combines great flexibility with an effective control of the various interactions in infinite dimensional systems.
MSC:
37J40Perturbations, normal forms, small divisors, KAM theory, Arnol’d diffusion
37J99Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
37J35Completely integrable systems, topological structure of phase space, integration methods
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
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