By B.A. Steves, A.J. Maciejewski, M. Hendry
In accordance with the hot NATO complicated research Institute "Chaotic Worlds: From Order to sickness in Gravitational N-Body Dynamical Systems", this state-of-the-art textbook, written through the world over well known specialists, presents a useful reference quantity for all scholars and researchers in gravitational n-body structures. The contributions are in particular designed to provide a scientific improvement from the elemental arithmetic which underpin smooth stories of ordered and chaotic behaviour in n-body dynamics to their program to genuine movement in planetary structures. This quantity provides an updated synoptic view of the topic.
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Extra info for Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems (NATO Science Series II: Mathematics, Physics and Chemistry)
However, there is a hidden parameter: it is the ratio |I ∗ |/ , where is the convergence radius of the Hamiltonian in Birkhoﬀ’s normal form. 6 An application to the Sun-Jupiter-Saturn system Applying the theorem of Kolmogorov to a real system is not an easy matter. Due to the very strong requests on the smallness of the parameter ε (that we have not reported for simplicity in the statement of theorem 4), even using the best available analytical estimates it is typical to end up with ridiculous results.
In Benest, D. , editors. Chaos and diﬀusion in Hamiltonian systems. Editions Fronti`eres. Giorgilli, A. and Locatelli, U. (1997a). Kolmogorov theorem and classical perturbation theory. ZAMP, 48:220–261. Giorgilli, A. and Locatelli, U. (1997b). On classical series expansions for quasi–periodic motions. MPEJ, 3(5). Giorgilli, A. and Morbidelli, A. (1997). Invariant KAM tori and global stability for Hamiltonian systems. ZAMP, 48:102–134. Giorgilli, A. and Locatelli, U. (1999). A classical self–contained proof of Kolmogorov’s theorem on invariant tori.
On classical series expansions for quasi–periodic motions. MPEJ, 3(5). Giorgilli, A. and Morbidelli, A. (1997). Invariant KAM tori and global stability for Hamiltonian systems. ZAMP, 48:102–134. Giorgilli, A. and Locatelli, U. (1999). A classical self–contained proof of Kolmogorov’s theorem on invariant tori. , editor. Hamiltonian systems with three or more degrees of freedom, NATO ASI series C, 533. Kluwer Academic Publishers, Dordrecht–Boston–London. Giorgilli, A. (2003). Notes on exponential stability of Hamiltonian systems.