相关论文: Renormalization theory for multimodal maps

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…

We describe all possible bimodal over-twist patterns. In particular, we give an algorithm allowing one to determine what the left endpoint of the over-rotation interval of a given bimodal map is. We then define a new class of polymodal…

We extend the renormalisation operator introduced in \cite{dCML} from period-doubling H\'enon-like maps to H\'enon-like maps with arbitrary stationary combinatorics. We show the renormalisation picture holds also holds in this case if the…

In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…

We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization…

We study the period doubling renormalization operator for dynamics which present two coupled laminar regimes with two weakly expanding fixed points. We focus our analysis on the potential point of view, meaning we want to solve…

Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…

In this short note, we propose to extend differentiability (with respect to a multidimensional parameter) of a normalized eigenfunction associated to the simple, dominating eigenvalue of the weighted transfer operator for a uniformly…

We consider holomorphic maps defined in an annulus around $\mathbb R/\mathbb Z$ in $\mathbb C/\mathbb Z$. E. Risler proved that in a generic analytic family of such maps $f_\zeta$ that contains a Brjuno rotation $f_0(z)=z+\alpha$, all 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…

Within the exact renormalisation group approach, it is shown that stability properties of the flow are controlled by the choice for the regulator. Equally, the convergence of the flow is enhanced for specific optimised choices for the…

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…

Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…

For each piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a $\beta$-transformation.

Various uses of the renormalization group are examined.

We construct a hyperbolic attractor of renormalization of bi-cubic circle maps with bounded combinatorics, with a codimension-two stable foliation.

This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…

We look at sections of a function bundle over the space of linear differential operators. We find that one can construct an isomorphism between a certain quotient bundle and the fourier counterpart of the original bundle defined by formal…

In this paper, we use iterations of skinning maps on Teichm\"uller spaces to study circle packings and develop a renormalization theory for circle packings whose nerves satisfy certain subdivision rules. We characterize when the skinning…

We present a novel approach for deriving KAM-type linearization theorems directly -- and almost immediately -- from the existence of the stable foliation for a renormalization operator. We give a few illustrations in dynamics in one and…