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