Related papers: Self semi conjugations of Ulam's Tent-map

Let $T$ be a measure preserving $\mathbb{Z}^\ell$-action on the probability space $(X,{\mathcal B},\mu),$ $q_1,\dots,q_m:{\mathbb R}\to{\mathbb R}^\ell$ vector polynomials, and $f_0,\dots,f_m\in L^\infty(X)$. For any $\epsilon > 0$ and…

In analogy with the semi-Fibonacci partitions studied recently by Andrews, we define semi-Pell compositions and semi-$m$-Pell compositions. We find that these are in bijection with certain weakly unimodal $m$-ary compositions. We give…

We resolve a conjecture of Cooper-Fenner-Purewal that a certain sequence of combinatorial matrices which can be used to bound small product-Ramsey numbers is positive semidefinite. Because the connection to Ramsey Theory involves solving…

We study linear difference equations with variable coefficients in a ring using a new nonlinear method. In a ring with identity, if the homogeneous part of the linear equation has a solution in the unit group of the ring (i.e., a unitary…

Given a semigroup $S$ and an $n$-partition $\mathcal{P}$ of $S$, $n\in \mathbb{N}$, do there exist $A\in \mathcal{P}$ and a subset $F$ of $S$ such that $S=F ^{-1} \{x \in S: x A \bigcap A\neq\emptyset\}$ and $|F |\leq n$? We give an…

We study the asymptotical behaviour of iterates of piecewise contractive maps of the interval. It is known that Poincar\'e first return maps induced by some Cherry flows on transverse intervals are, up to topological conjugacy, piecewise…

We consider Lie groups ${\rm SU}(n,1)$ and ${\rm Sp}(n,1)$ that act as the isometries of the complex and quaternionic hyperbolic spaces respectively. We classify pairs of semisimple elements in ${\rm Sp}(n,1)$ and ${\rm SU}(n,1)$ up to…

Let A be a finite-dimensional associative algebra and $\phi$ a symmetric linear function on $A$. In this note, we will show that the pseudotrace maps are obtained as special cases of well-known symmetric linear functions on the endomorphism…

A symmetric tensor may be regarded as a partially symmetric tensor in several different ways. These produce different notions of rank for the symmetric tensor which are related by chains of inequalities. By exploiting algebraic tools such…

It is well-known that an element of the linear group ${\rm GL}_n(\C)$ is semisimple if and only if its conjugacy class is Zariski closed. The aim of this paper is to show that the same result holds for the group of complex plane polynomial…

By rewriting the famous hook-content formula it easily follows that there are $\prod\limits_{1 \le i < j \le n} \frac{k_j - k_i + j -i}{j-i}$ semistandard tableaux of shape $(k_n,k_{n-1},...,k_1)$ with entries in $\{1,2,...,n\}$ or,…

Let $M_n$ be a $n \times n$ Wigner or sample covariance random matrix, and let $\mu_1(M_n), \mu_2(M_n), ..., \mu_n(M_n)$ denote the unordered eigenvalues of $M_n$. We study the fluctuations of the partial linear eigenvalue statistics $$…

We show that a continuous map $f$ from a quasi-graph $G$ to itself is pointwise recurrent if and only if one of the following two statements holds: (1) $X$ is a simple closed curve and $f$ is topologically conjugate to an irrational…

We present results about the Cantor-Bendixson index of some subspaces of a uniform family F of finite subsets of natural numbers with respect to the lexicographic order topology. As a corollary of our results we get that for any…

Let $S$ and $T$ be subsets of $\mathbf{F}_q^n$. We show there are subsets $S'$ of $S$ and $T'$ of $T$ such that $S+T$ is the union of $S+T'$ and $S'+T$, with $|S'| + |T'|$ bounded by $c^n$ with $c < q$. The proof relies on the method of…

We prove the existence of Cannon-Thurston maps for Kleinian groups corresponding to pared manifolds whose boundary is incompressible away from cusps. We also describe the structure of these maps in terms of ending laminations.

In this paper, we provide new discrete uniformization theorems for bounded, $m$-connected planar domains. To this end, we consider a planar, bounded, $m$-connected domain $\Omega$ and let $\bord\Omega$ be its boundary. Let $\mathcal{T}$…

Given a semigroup $S$ and $s,t \in S$, write $s \sim_p^1 t$ if $s=pr$ and $t=rp$, for some $p,r \in S \cup \{1\}$. This relation, known as "primary conjugacy", along with its transitive closure $\sim_p$, has been extensively used and…

An $\alpha$-thin tree $T$ of a graph $G$ is a spanning tree such that every cut of $G$ has at most an $\alpha$ proportion of its edges in $T$. The Thin Tree Conjecture proposes that there exists a function $f$ such that for any $\alpha >…

In this article, we define the Coifman-Meyer-Stein tent spaces $T^{p,q,\alpha}(X)$ associated with an arbitrary metric measure space $(X,d,\mu)$ under minimal geometric assumptions. While gradually strengthening our geometric assumptions,…