Related papers: The periodic points of renormalization

We study the dynamics of the renormalization operator acting on the space of pairs (v,t), where v is a diffeomorphism and t belongs to [0,1], interpreted as unimodal maps x-->v(q_t(x)), where q_t(x)=-2t|x|^a+2t-1. We prove the so called…

We define an analytic setting for renormalization of unimodal maps with an arbitrary critical exponent. We prove the global Hyperbolicity of Renormalization conjecture for unimodal maps of bounded type with a critical exponent which is…

We first give a condition for a normal operator on a Hilbert space to have no nonzero periodic points, then we give a characterization of normal operators with the whole space as periodic points. We proceed to study the structure of…

We present a proof of the existence of a renormalization fixed point for Lorenz maps of the simplest non-unimodal combinatorial type ({0,1},{1,0,0}), and with a critical point of arbitrary order rho>1.

We consider infinitely renormalizable unimodal mappings with topological type which is periodic under renormalization. We study the limiting behavior of fixed points of the renormalization operator as the order of the critical point…

We consider infinitely renormalizable Lorenz maps with real critical exponent $\alpha>1$ and combinatorial type which is monotone and satisfies a long return condition. For these combinatorial types we prove the existence of periodic points…

We study the dynamics of the renormalization operator for multimodal maps. In particular, we prove the exponential convergence of this operator for infinitely renormalizable maps with same bounded combinatorial type.

Lorenz maps are maps of the unit interval with one critical point of order rho>1, and a discontinuity at that point. They appear as return maps of leafs of sections of the geometric Lorenz flow. We construct real a priori bounds for…

In this paper we give a combinatorial description of the renormlization limits of infinitely renormalizable unimodal maps with {\it essentially bounded} combinatorics admitting quadratic-like complex extensions. As an application we…

We prove the existence of fixed points of p-tupling renormalization operators for interval and circle mappings having a critical point of arbitrary real degree r > 1. Some properties of the resulting maps are studied: analyticity,…

We study circle maps with a flat interval where the critical exponents at the two boundary points of the flat spot might be different. The space of such systems is partitioned in two connected parts whose common boundary only depends on the…

We prove that any unicritical polynomial $f_c:z\mapsto z^d+c$ which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. It implies that the connectedness locus (the ``Multibrot set'') is…

For an infinitely renormalizable negative Schwarzian unimodal map $f$ with non-flat critical point, we analyze statistical properties of periodic points as the periods tend to infinity. Introducing a weight function $\varphi$ which is a…

A Lorenz map is a Poincar\'e map for a three-dimensional Lorenz flow. We describe the theory of renormalization for Lorenz maps with a critical point and prove that a restriction of the renormalization operator acting on such maps has a…

We study the phenomenon of composite operator renormalization and mixing in systems where time-translational invariance is broken and the evolution is out-of-equilibrium. We show that composite operators mix also through non-local memory…

We study the critical behavior of period doubling in two coupled one-dimensional maps with a single maximum of order $z$. In particurlar, the effect of the maximum-order $z$ on the critical behavior associated with coupling is investigated…

This paper deals with the renormalization of symmetric bimodal maps with low smoothness. We prove the existence of the renormalization fixed point in the space $C^{1+Lip}$ symmetric bimodal maps. Moreover, we show that the topological…

In this paper we generalize renormalization theory for analytic critical circle maps with a cubic critical point to the case of maps with an arbitrary odd critical exponent by proving a quasiconformal rigidity statement for renormalizations…

Given $C^2$ infinitely renormalizable unimodal maps $f$ and $g$ with a quadratic critical point and the same bounded combinatorial type, we prove that they are $C^{1+\alpha}$ conjugate along the closure of the corresponding forward orbits…

We gain tight rigorous bounds on the renormalisation fixed point for period doubling in families of unimodal maps with degree $4$ critical point. We use a contraction mapping argument to bound essential eigenfunctions and eigenvalues for…