A Semi-Classical K.A.M. Theorem
نویسندگان
چکیده
منابع مشابه
A semi-classical K.A.M. theorem
We consider a semi-classical completely integrable system defined by a ~-pseudodifferential operator Ĥ on the torus T. In order to study perturbed operators of the form Ĥ + ~K̂ , where K̂ is an arbitrary pseudodifferential operator and κ > 0, we prove the conjugacy to a suitable normal form. This is then used to construct a large number of quasimodes.
متن کاملAn analytic KAM-Theorem
We prove an analytic KAM-theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the theorem presented here is to provide exactly the estimates needed in [1].
متن کاملKam Theorem Revisited
A terse direct proof of the KAM theorem in the Thirring model is presented, by using a multiscale decomposition technique usual in quantum eld theory formalism. The KAM theorem proves in a indirect way that the formal perturbation series for the invariant tori of quasi integrable systems are convergent, if some conditions are fulllled by the hamiltonian. Of course one should be able to prove th...
متن کاملNotes on the KAM theorem
I hope eventually to expand these notes into a standalone presentation of KAM that presents a precise formulation of the theorem and gives detailed proofs of everything. There are few presentations of KAM in the literature that give a precise formulation of the theorem, and even those that give precise formulations such as [6] and [7] glide over some details. Gallavotti [4] explains the history...
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ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2007
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605300600856915