Related papers: Siegel disks and renormalization fixed points

Bounded irreducible local Siegel disks include classical Siegel disks of polynomials, bounded irreducible Siegel disks of rational and entire functions, and the examples of Herman and Moeckel. We show that there are only two possibilities…

In this paper we give a new prove of hyperbolicity of renormalization of critical circle maps using the formalism of almost-commuting pairs. We extend renormalization to two-dimensional dissipative maps of the annulus which are small…

We show that a large class of gapless states are renormalization group fixed points in the sense that they can be grown scale by scale using local unitaries. This class of examples includes some theories with dynamical exponent different…

We consider the parabolic-elliptic Keller-Segel system in spatial dimensions $d\geq3$, which corresponds to the mass supercritical case. Some solutions become singular in finite time, an important example being backward self-similar…

We consider the renormalization of d-dimensional hypersurfaces (branes) embedded in flat (d+1)-dimensional space. We parametrize the truncated effective action in terms of geometric invariants built from the extrinsic and intrinsic…

Macbeath gave a formula for the number of fixed points for each non-identity element of a cyclic group of automorphisms of a compact Riemann surface in terms of the universal covering transformation group of the cyclic group. We observe…

We discuss an alternative approach to the uniformisation problem on surfaces with boundary by representing conformal structures on surfaces $M$ of general type by hyperbolic metrics with boundary curves of constant positive geodesic…

We investigate the renormalization group flows and fixed point structure of many coupled minimal models. The models are coupled two by two by energy-energy couplings. We take the general approach where the bare couplings are all taken to be…

A new construction is presented of scalar-flat Kaehler metrics on non-minimal ruled surfaces. The method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank-2 parabolically stable…

A neutral fixed point of a real iteration map $u$ becomes a super attracting fixed point using a suitable double newtonisation. The map $u$ is so transformed into a map $w$ which is here called the standard accelerator of $u$. The map $w$…

For some special window functions $\psi_{\beta} \in H^2(\mathbb{C}^+),$ we prove that, over all sets $\Delta \subset \mathbb{C}^+$ of fixed hyperbolic measure $\nu(\Delta),$ the ones over which the Wavelet transform…

We prove that if two non-renormalizable cubic Siegel polynomials with bounded type rotation numbers are combinatorially equivalent, then they are also conformally equivalent. As a consequence, we show that in the one-parameter slice of…

Given a closed hyperbolic surface $S$, let $\cQF$ denote the space of quasifuchsian hyperbolic metrics on $S\times\R$ and $\cGH_{-1}$ the space of maximal globally hyperbolic anti-de Sitter metrics on $S\times\R$. We describe natural maps…

We give normal forms for strongly hyperbolic logarithmic transseries f = z^r + ... (r is a positive real number nonequal to 1), with respect to parabolic logarithmic normalizations. These normalizations are obtained using fixed point…

In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…

This work constructs symbolic dynamics for non-uniformly hyperbolic surface maps with a set of discontinuities $D$. We allow the derivative of points nearby $D$ to be unbounded, of the order of a negative power of the distance to $D$. Under…

Inou and Shishikura provided a class of maps that is invariant by near-parabolic renormalization, and that has proved extremely useful in the study of the dynamics of quadratic polynomials. We provide here another construction, using more…

We construct symplectic blenders for two classical Hamiltonian systems: the 3-body problem and its restricted version. We use these objects to show that both models exhibit a robust, strong form of topological instability. We do not assume…

In this article we explore the relationship between the systole and the diameter of closed hyperbolic orientable surfaces. We show that they satisfy a certain inequality, which can be used to deduce that their ratio has a (genus dependent)…

We calculate the asymptotic average rate at which a generic geodesic on a finite area hyperbolic 2-orbifold returns to an embedded disc on the surface, as well as the average amount of time it spends in the disc during each visit. This…