Related papers: Rescaling Limits in Non-Archimedean Dynamics

Finite-size critical systems defined on a parallel plate geometry of finite extent along one single ($z$) direction with Dirichlet and Neumann boundary conditions at $z=0,L$ are analyzed in momentum space. We introduce a modified…

Let k be an algebraically closed field complete with respect to a non-Archimedean absolute value of arbitrary characteristic. Let D_1,...,D_n be effective nef divisors intersecting transversally in an n-dimensional nonsingular projective…

We show that the finiteness length of an $S$-arithmetic subgroup $\Gamma$ in a noncommutative isotropic absolutely almost simple group $G$ over a global function field is one less than the sum of the local ranks of $G$ taken over the places…

We study structural limitations of purely algebraic reasoning in the analysis of arithmetic dynamical systems. Rather than addressing the truth of specific conjectures, we introduce a fragment - relative notion of algebraic refutability for…

When $R$ is a non-archimedean real closed field we say that a function $f\in R(\bar{X})$ is finitary at a point $\bar{b}\in R^n$ if on some neighborhood of $\bar{b}$ the defined values of $f$ are in the finite part of $R$. In this note we…

We consider when finite families $F \subseteq \mathbb{C}[t]$ of bounded degree polynomials, or more generally of bounded complexity finite-to-finite correspondences on $\mathbb{C}$, can exhibit non-expansion of the form $|F(A)| =…

Let $\mathbb{C}_K$ be a complete and algebraic closed non-archimedean field with residual characteristic $2$. In this paper we prove that there exist $a,b\in\mathbb{C}_K$ such that the rational function $R(z)=\frac{z^2-z}{bz-\frac{1}{a}}$…

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, i.e.\ operators whose range are sets…

A family $f_t(z)$ of polynomials over a number field $K$ will be called \emph{weighted homogeneous} if and only if $f_t(z)=F(z^e, t)$ for some binary homogeneous form $F(X, Y)$ and some integer $e\geq 2$. For example, the family $z^d+t$ is…

We define an analytic setting for renormalization of unimodal maps with an arbitrary critical exponent. We prove the global Hyperbolicity of Renormalization conjecture for unimodal maps of bounded type with a critical exponent which is…

An extension of algebras is a homomorphism of algebras preserving identities. We use extensions of algebras to study the finitistic dimension conjecture over Artin algebras. Let $f: B \to A$ be an extension of Artin algebras. We denote by…

This paper examines fields of rationality in families of cuspidal automorphic representations of unitary groups. Specifically, for a fixed $A$ and a sufficiently large family $\mathcal{F}$, a small proportion of representations $\pi\in…

We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one…

The smallness is proved of fundamental groups for arithmetic schemes. This is a higher dimensional analogue of the Hermite-Minkowski theorem. We also refer to the case of varieties over finite fields. As an application, we prove certain…

We prove a reduction theorem for capacity of positive maps of finite dimensional C*-algebras, thus reducing the computation of capacity to the case when the image of a nonscalar projection is never a projection.

For equivariant stable homotopy theory, equivariant KK-theory and equivariant derived categories, we show how restriction to a subgroup of finite index yields a finite commutative separable extension, analogous to finite \'etale extensions…

We describe a theory of finite sets, and investigate the analogue of Dedekind's theory of natural number systems (simply infinite systems) in this theory. Unlike the infinitary case, in our theory, natural number systems come in differing…

We present a study of the problem of finiteness of the $\beta$-expansions for the set of natural numbers, condition $F_1$ in brief, for three families of Pisot numbers for which the $\beta$-expansion of 1 is not a non-decreasing sequence.…

In this work, we introduce a natural notion concerning finite vector spaces. A family of $k$-dimensional subspaces of $\mathbb{F}_q^n$, which forms a partial spread, is called almost affinely disjoint if any $(k+1)$-dimensional subspace…

For a field K, rational function phi in K(z) of degree at least two, and alpha in P^1(K), we study the polynomials in K[z] whose roots are given by the solutions to phi^n(z) = alpha, where phi^n denotes the nth iterate of phi. When the…