Quasi-effective stability for nearly integrable Hamiltonian systems
نویسندگان
چکیده
منابع مشابه
On the stability problem for nearly{integrable Hamiltonian systems
The problem of stability of the action variables in nearly{integrable (real{ analytic) Hamiltonian systems is considered. Several results (fully described in CG2]) are discussed; in particular: (i) a generalization of Arnold's method (A]) allowing to prove instability (i.e. drift of action variables by an amount of order 1, often called \Arnold's diiusion") for general perturbations of \a{prior...
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In the 70’s, Nekhorochev proved that for an analytic nearly integrable Hamiltonian system, the action variables of the unperturbed Hamiltonian remain nearly constant over an exponentially long time with respect to the size of the perturbation, provided that the unperturbed Hamiltonian satisfies some generic transversality condition known as steepness. Recently, Guzzo has given examples of expon...
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Nekhoroshev's theorem on the stability of motions in quasi-integrable Hamiltonian systems is revisited. At variance with the proofs already available in the literature, we explicitly consider the case of weakly perturbed harmonic oscillators; furthermore we prove the confinement of orbits in resonant regions, in the general case of nonisochronous systems, by using the elementary idea of energy ...
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A notion of instability, which is proposed as a deenition for the so{called \Arnold diiusion", for one{parameter families of nearly{integrable analytic Hamiltonian systems, is introduced. An example of unstable system is given.
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We obtain a global version of the Hamiltonian KAM theorem for invariant Lagrangean tori by glueing together local KAM conjugacies with help of a partition of unity. In this way we find a global Whitney smooth conjugacy between a nearly integrable system and an integrable one. This leads to preservation of geometry, which allows us to define all nontrivial geometric invariants of an integrable H...
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems - Series B
سال: 2015
ISSN: 1531-3492
DOI: 10.3934/dcdsb.2016.21.67