Related papers: Dynamical properties of critical exponent function…

The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…

Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in…

We give an alternative proof of the Benedicks-Carleson theorem on the existence of strange attractors in H\'enon-like families in the plane. To bypass a huge inductive argument, we introduce an induction-free explicit definition of…

A surprising result of FitzGerald and Horn (1977) shows that $A^{\circ \alpha} := (a_{ij}^\alpha)$ is positive semidefinite (p.s.d.) for every entrywise nonnegative $n \times n$ p.s.d. matrix $A = (a_{ij})$ if and only if $\alpha$ is a…

We introduce a discrete dynamical system on the integers, defined by moving a composite $m$ forward to $m+\pi(m)$ and a prime $p$ backward to $p-\mathrm{prevprime}(p)$. This map produces trajectories whose contraction properties are closely…

In the early 1980's Thurston gave a topological characterization of rational maps whose critical points have finite iterated orbits (\cite{Th,DH1}): given a topological branched covering $F$ of the two sphere with finite critical orbits, if…

We prove strong statistical stability of a large class of one-dimensional maps which may have an arbitrary finite number of discontinuities and of non-degenerate critical points and/or singular points with infinite derivative, and satisfy…

For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of…

The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is…

This continues the investigation of a combinatorial model for the variation of dynamics in the family of rational maps of degree two, by concentrating on those varieties in which one critical point is periodic. We prove some general results…

We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the…

The robustness of the universality class concept of the chaotic transition was investigated by analytically obtaining its critical exponent for a wide class of maps. In particular, we extended the existing one-dimensional chaotic maps,…

We review the combinatorial, topological, algebraic and metric properties supported by $(D+1)$-colored graphs, with a focus on those that are pertinent to the study of tensor model theories. We show how to extract a limiting continuum…

In this work, we relate the geometry of chaotic attractors of typical analytic unimodal maps to the behavior of the critical orbit. Our main result is an explicit formula relating the combinatorics of the critical orbit with the exponents…

We consider dynamical systems given by interval maps with a finite number of turning points (including critical points, discontinuities) possibly of different critical orders from two sides. If such a map $f$ is continuous and piecewise…

The Epstein deformation space parameterizes marked rational maps with prescribed combinatorial and dynamical structure. For the family of quadratic rational maps with a periodic critical cycle of order 4 and an extra critical point not…

We investigate the asymptotic and effective static and dynamic critical behavior of (d=3)-dimensional magnets with quenched extended defects, correlated in $\epsilon_d$ dimensions (which can be considered as the dimensionality of the…

Given any n-tuple of complex numbers, one can canonically define a polynomial of degree n+1 that has the entries of this n-tuple as its critical points. In 2002, Beardon, Carne, and Ng studied a map $\theta\colon \mathbb{C}^n\to…

We study the dynamic critical exponent from effective and microscopic theories. We employ a simple TDGL model, or model A in the classification of Hohenberg and Halperin, as an effective theory and the imaginary time formalism of the…

Exploiting the indistinguishability of objects in a probabilistic graphical model such as a factor graph is key to lifted probabilistic inference algorithms and allows for tractable probabilistic inference problems with respect to domain…