Related papers: Renormalization of bi-cubic circle maps
After proving a multi-dimensional extension of Zalcman's renormalization lemma and considering maximality problems about dimensions, we find renormalizing polynomial families for iterated elementary mappings, extending this result to some…
Renormalization group limit cycles may be a commonplace for quantum Hamiltonians requiring renormalization, in contrast to experience to date with classical models of critical points, where fixed points are far more common. We discuss the…
We provide a computer-assisted proof of one of the central open questions in one-dimensional renormalization theory -- universality of the golden-mean Siegel disks. We further show that for every function in the stable manifold of the…
We study the scaling behavior of period doublings in two unidirectionally-coupled one-dimensional maps near a bicritical point where two critical lines of period-doubling transition to chaos in both subsystems meet. Note that the bicritical…
We construct an approximate renormalization for Hamiltonian systems with two degrees of freedom in order to study the break-up of invariant tori with arbitrary frequency. We derive the equation of the critical surface of the renormalization…
We show that there is a bijection between the renormalizations and proper completely invariant closed sets of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. Based on the properties of…
Parabolic renormalization associates to a holomorphic map f with a parabolic fixed point another holomorphic map with a parabolic fixed point. This procedure is essential for understanding the phenomenon of parabolic enrichment, which…
We present an inverse problem which uses the renormalized area functional on minimal submanifolds to recover the expansion of asymptotically hyperbolic, conformally compact metrics which are partially even to high order. We use a rigidity…
In this paper we establish $C^2$ a-priori bounds for the scaling ratios of critical circle mappings in a form that gives also a compactness property for the renormalization operator.
We prove that if two analytic multicritical circle maps with the same bounded type rotation number are topologically conjugate by a conjugacy which matches the critical points of the two maps while preserving the orders of their…
Given a holomorphic regularisation procedure (e.g. Riesz or dimensional regularisation) on classical symbols, we define renormalised multiple integrals of radial classical symbols with linear constraints. To do so, we first prove the…
Area-preserving maps have been observed to undergo a universal period-doubling cascade, analogous to the famous Feigenbaum-Coullet-Tresser period doubling cascade in one-dimensional dynamics. A renormalization approach has been used by…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
Two proofs of the Central Limit Theorem using a renormalization group approach are presented. The first proof is conducted under a third moment assumption and shows that a suitable renormalization group map is a contraction over the space…
We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…
In this note we construct hyperbolic fixed points for cylinder renormalization of maps with Siegel disks.
We give a comprehensive review of the renormalization group method for global and asymptotic analysis, putting an emphasis on the relevance to the classical theory of envelopes and the existence of invariant manifolds of the dynamics under…
Using the machinery of smooth scaling and coarse-graining of observables, developed recently in the context of so-called fluctuation operators (originally developed by Verbeure et al), we extend this approach to a rigorous renormalisation…
In this paper, we construct geometrically finite rational maps with buried critical points on the boundaries of some hyperbolic components by using the pinching and plumbing deformations.
In this paper we describe the well studied process of renormalization of quadratic polynomials from the point of view of their natural extensions. In particular, we describe the topology of the inverse limit of infinitely renormalizable…