7,687 research outputs found
Methods for the analysis of the Lindstedt series for KAM tori and renormalizability in classical mechanics
This paper consists in a unified exposition of methods and techniques of the
renormalization group approach to quantum field theory applied to classical
mechanics, and in a review of results: (1) a proof of the KAM theorem, by
studing the perturbative expansion (Lindstedt series) for the formal solution
of the equations of motion; (2) a proof of a conjecture by Gallavotti about the
renormalizability of isochronous hamiltonians, i.e. the possibility to add a
term depending only on the actions in a hamiltonian function not verifying the
anisochrony condition so that the resulting hamiltonian is integrable. Such
results were obtained first by Eliasson; however the difficulties arising in
the study of the perturbative series are very similar to the problems which one
has to deal with in quantum field theory, so that the use the methods which
have been envisaged and developed in the last twenty years exactly in order to
solve them allows us to obtain unified proofs, both conceptually and
technically. In the final part of the review, the original work of Eliasson is
analyzed and exposed in detail; its connection with other proofs of the KAM
theorem based on his method is elucidated.Comment: 58, compile with dvips to get the figure
Melnikov's approximation dominance. Some examples
We continue a previous paper to show that Mel'nikov's first order formula for
part of the separatrix splitting of a pendulum under fast quasi periodic
forcing holds, in special examples, as an asymptotic formula in the forcing
rapidity.Comment: 46 Kb; 9 pages, plain Te
Homoclinic splitting, II. A possible counterexample to a claim by Rudnev and Wiggins on Physica D
Results in the mentioned paper do not seem valid.Comment: 2 pages, plain Te
Pendulum: separatrix splitting
An exact expression for the determinant of the splitting matrix is derived:
it allows us to analyze the asympotic behaviour needed to amend the large
angles theorem proposed in Ann. Inst. H. Poincar\'e, B-60, 1, 1994. The
asymptotic validity of Melnokov's formulae is proved for the class of models
considered, which include polynomial perturbations.Comment: 30 pages, one figur
Pervasive Displays Research: What's Next?
Reports on the 7th ACM International Symposium on Pervasive Displays that took place from June 6-8 in Munich, Germany
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