Related papers: Renormalization of bi-cubic circle maps
The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…
Holomorphic renormalization plays an important role in complex polynomial dynamics. We consider certain conditions guaranteeing that a polynomial which does not admit a polynomial-like connected Julia set still admits an invariant continuum…
The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with…
A gap mapping is a discontinuous interval mapping with two strictly increasing branches that have a gap between their ranges. They are one-dimensional dynamical systems, which arise in the study of certain higher dimensional flows, for…
We consider circles of common centre and increasing radius on a compact hyperbolic surface and, more generally, on its unit tangent bundle. We establish a precise asymptotics for their rate of equidistribution. Our result holds for…
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…
We prove a topological rigidity result for simple, thick, hyperbolic P-manifolds of dimension 2: isomorphism of the fundamental groups implies homeomorphism of the P-manifolds. An immediate application is a diagram rigidity theorem for…
We solve analytically the renormalization-group equation for the potential of the O(N)-symmetric scalar theory in the large-N limit and in dimensions 2<d<4, in order to look for nonperturbative fixed points that were found numerically in a…
We introduce a renormalization procedure which allows us to study in a unified and concise way different properties of the irrational rotations on the unit circle $\beta \mapsto \set{\alpha+\beta}$, $\alpha \in \R\setminus \Q$. In…
We develop a renormalization group for weak Harris-marginal disorder in otherwise strongly interacting quantum critical theories, focusing on systems which have emergent conformal invariance. Using conformal perturbation theory, we argue…
We classify real two-dimensional orbits of conformal subgroups such that the orbits contain two circular arcs through a point. Such surfaces must be toric and admit a M\"obius automorphism group of dimension at least two. Our theorem…
We show that limits for the critical exponent tending to \infty exist in both critical circle homeomorphisms of golden mean rotation number and Fibonacci circle coverings. Moreover, they are the same. The limit map is not analytic at the…
A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the…
This paper presents a survey of recent and not so recent results concerning the study of smooth homeomorphisms of the circle with a finite number of non-flat critical points, an important topic in the area of One-dimensional Dynamics. We…
Let $f: S^1\to S^1$ be a $C^3$ homeomorphism without periodic points having a finite number of critical points of power-law type. In this paper we establish real a-priori bounds, on the geometry of orbits of $f$, which are beau in the sense…
As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is…
We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…
An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points…
A plausible physical interpretation of the renormalizability condition is given. It is shown that renormalizable quantum field theories describe such systems wherein the tendency to collapse associated with vacuum fluctuations of attractive…
A holomorphic endomorphism of $\mathbb{CP}^n$ is post-critically algebraic if its critical hypersurfaces are periodic or preperiodic. This notion generalizes the notion of post-critically finite rational maps in dimension one. We will study…