Related papers: The fixed point of the parabolic renormalization o…
We consider the continuum parabolic Anderson model (PAM) and the dynamical $\Phi^4$ equation on the $3$-dimensional cube with boundary conditions. While the Dirichlet solution theories are relatively standard, the case of Neumann/Robin…
Based on the Cornwall-Jackiw-Tomboulis effective potential, we extensively study nonperturbative renormalization of the gauged Nambu-Jona-Lasinio model in the ladder approximation with standing gauge coupling. Although the pure…
We analyse the renormalisation group flow of quantum gravity at sixth order in the derivative expansion within the background field approximation. Non-linear field redefinitions are used to ensure that only essential couplings flow. Working…
In the framework of the 1/N-expansion we show that the Callan-Symanzik beta- function associated with the four-point coupling g is non-analytic at its zero, i.e. at the fixed-point value g^* of g. This behavior can be interpreted by…
We investigate possible renormalization-group fixed points at nonzero coupling in $\phi^3$ theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three theories of this type, with (a) a…
We prove exponential contraction of renormalization along hybrid classes of infinitely renormalizable unimodal maps (with arbitrary combinatorics), in any even degree $d$. We then conclude that orbits of renormalization are asymptotic to…
We consider a one-parameter family of piecewise isometries of a rhombus. The rotational component is fixed, and its coefficients belong to the quadratic number field $K=\mathbb{Q}(\sqrt{2})$. The translations depend on a parameter $s$ which…
We study renormalization group (RG) fixed points of scalar field theories endowed with the discrete symmetry groups of regular polytopes. We employ the functional perturbative renormalization group (FPRG) approach and the…
Three dimensional analytic H\'enon-like map $$ F(x,y,z) = (f(x) - \epsilon(x,y,z),\, x,\, \delta(x,y,z)) $$ and its {\em period doubling} renormalization is defined. If $ F $ is infinitely renormalizable map, Jacobian determinant of $…
We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension~$k$ (i.e.~a fixed point of multiplicity $k+1$) under conjugacy. Such generic unfoldings depend real analytically on $k$ real…
Given $\alpha \in (0, \infty)$ and $r \in (0, \infty)$, let ${\cal D}_{r, \alpha}$ be the disc of radius $r$ in the hyperbolic plane having curvature $-\alpha^2$. Consider the Poisson point process having uniform intensity density on ${\cal…
We study the fixed point set in the ideal boundary of a parabolic isometry of a proper CAT(0)-space. We show that the radius of the fixed point set is at most pi/2, and study its centers. As a consequence, we prove that the set of fixed…
In this paper, we consider the finite element approximation for a parabolic problem on a smooth domain $\Omega \subset \mathbb{R}^N$ with the inhomogeneous Neumann boundary condition. We emphasize that the domain can be non-convex in…
Let $\mathbb{X}$ be a Jordan domain satisfying hyperbolic growth conditions. Assume that $\varphi$ is a homeomorphism from the boundary $\partial \mathbb{X}$ of $\mathbb{X}$ onto the unit circle. Denote by $h$ the harmonic diffeomorphic…
Within the framework of the renormalization group approach in the stochastic model of fully developed turbulence, the $\beta$-function has been calculated in the fourth order of perturbation theory for high-dimensional spaces $d \rightarrow…
We find renormalization group transformations for the compactified Randall-Sundrum scenario by integrating out an infinitesimal slice of ultraviolet degrees of freedom near the Planck brane. Under these transformations the coefficients of…
Let $P$ be a polynomial of degree $d$ with Julia set $J_P$. Let $\widetilde N$ be the number of non-repelling cycles of $P$. By the famous Fatou-Shishikura inequality $\widetilde N\le d-1$. The goal of the paper is to improve this bound.…
The main purpose of this work is to extend the properties of multivalued transformations to the integral type transformations and to obtain the existence of fixed points under F-contraction. In addition, the results of this study were…
Let P be a non-linear polynomial, K_P the filled Julia set of P, f a renormalization of P and K_f the filled Julia set of f. We show, loosely speaking, that there is a finite-to-one function \lambda from the set of P-external rays having…
We develop a Thurston-like theory to characterize geometrically finite rational maps, then apply it to study pinching and plumbing deformations of rational maps. We show that in certain conditions the pinching path converges uniformly and…