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RESEARCH PRODUCT

The KAM Theorem

Walter DittrichMartin Reuter

subject

Pure mathematicsIterated functionKolmogorov–Arnold–Moser theoremPerturbation (astronomy)TorusLinear independenceMathematicsTwo degrees of freedom

description

This theorem guarantees that, under certain assumptions, in the case of a perturbation \(\varepsilon H_{1}(\boldsymbol{J},\boldsymbol{\theta })\) with small enough ɛ, the iterated series for the generator W(θ i 0, J i ) converges (according to Newton’s procedure) and thus the invariant tori are not destroyed. The KAM theorem is valid for systems with two and more degrees of freedom. However, in the following, we shall deal exclusively with the case of two degrees of freedom.

yearjournalcountryeditionlanguage
2016-01-01
https://doi.org/10.1007/978-3-319-21677-5_16