Scaling, Perturbative Renormalization and Analyticity for the Standard Map and Some Generalizations
نویسنده
چکیده
We summarize some numerical works on the analyticity properties of the perturbative series (e. g. Lindstedt series) for some simple discrete-time hamiltonian systems like the so-called \standard map" and generalizations. We stress the relevance of our results for the development of a renormalization group picture based on perturbation theory.
منابع مشابه
Renormalization Group and Field Theoretic Techniques for the Analysis of the Lindstedt Series
The Lindstedt series were introduced in the XIX century in Astronomy to study perturbatively quasi-periodic motions in Celestial Mechanics. In Mathematical Physics, after getting the attention of Poincaré, who studied them widely by pursuing to all orders the analysis of Lindstedt and Newcomb, their use was somehow superseded by other methods usually referred to as KAM theory. Only recently, af...
متن کاملComputation of the breakdown of analyticity in statistical mechanics models: numerical results and a renormalization group explanation
We consider one dimensional systems of particles interacting with each other through long range interactions that are translation invariance. We seek quasi-periodic equilibrium states. Standard arguments show that if there are continuous families of quasi-periodic ground states, the system can have large scale motion, if the family of ground states is discontinuous, the system is pinned down. T...
متن کاملRub-tpii-16/05 Improving Qcd Perturbative Predictions and Transverse Momentum Effects
I elaborate on the implementation of analyticity of hadronic quantities at the amplitude level and show that it amounts to the extension of Analytic Perturbation Theory of Shirkov and Solovtsov to non-integer (fractional) powers of the strong running coupling. I give evidence that at the NLO of the factorized pion’s electromagnetic form factor this framework diminishes the uncertainty due to th...
متن کاملPeriod Doubling Renormalization for Area-Preserving Maps and Mild Computer Assistance in Contraction Mapping Principle
A universal period doubling cascade analogous to the famous FeigenbaumCoullet-Tresser period doubling has been observed in area-preserving maps of R. Existence of the “universal” map with orbits of all binary periods has been proved via a renormalization approach in (Eckmann et al 1984) and (Gaidashev et al 2011). These proofs use “hard” computer assistance. In this paper we attempt to reduce c...
متن کاملOn the singularity structure of invariant curves of symplecticmappings . 1
We study invariant curves in standard-like maps conjugate to rigid rotation with complex frequencies. The main goal is to study the analyticity domain of the functions deened perturbatively by Lindstedt perturbation expansions. We argue, based on innnite-dimensional bifurcation theory that the boundary of analyticity should typically consist of branch points of order two and we verify it in som...
متن کامل