Related papers: Understanding the limit sets generated by general …
We consider iterated function systems $\mathrm{IFS}(T_1,\dots,T_k)$ consisting of continuous self maps of a compact metric space $X$. We introduce the subset $S_{\mathrm{t}}$ of {\emph{weakly hyperbolic sequences}} $\xi=\xi_0\ldots\xi_n…
The estimation of categorical distributions under marginal constraints summarizing some sample from a population in the most-generalizable way is key for many machine-learning and data-driven approaches. We provide a parameter-agnostic…
Implicit networks are a class of neural networks whose outputs are defined by the fixed point of a parameterized operator. They have enjoyed success in many applications including natural language processing, image processing, and numerous…
Following the work of Louisa and Michael Barnsley on results in tops of iterated function systems, we extend their work to graph-directed iterated function systems by investigating the relationship between top addresses and shift spaces.…
Given an infinite iterated function system (IFS) $\mathcal{F}$, we define its dimension spectrum $D(\mathcal{F})$ to be the set of real numbers which can be realised as the dimension of some subsystem of $\mathcal{F}$. In the case where…
We reformulate and generalize the uniqueness and existence proofs of time-dependent density-functional theory. The central idea is to restate the fundamental one-to-one correspondence between densities and potentials as a global fixed point…
Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded…
We study the topological properties of attractors of Iterated Function Systems (I.F.S.) on the real line, consisting of affine maps of homogeneous contraction ratio. These maps define what we call a second generation I.F.S.: they are…
We present a mathematical model: dynamical systems over finite sets (DSF), and we show that Boolean and discrete genetic models are special cases of DFS. In this paper, we prove that a function defined over finite sets with different number…
We introduce a notion of integration defined from filters over families of finite sets. This procedure corresponds to determining the average value of functions whose range lies in any algebraic structure in which finite averages make…
This work is devoted to the study of families of infinite parabolic iterated function systems (PIFS) on a closed interval parametrized by vectors in $\mathbb{R}^d$ with overlaps. We show that the Hausdorff dimension and absolute continuity…
In this note, we consider a framework for the analysis of iterative algorithms which can described in terms of a structured set-valued operator. More precisely, at each point in the ambient space, we assume that the value of operator can be…
In this article, we further develop the thermodynamic formalism of affine iterated function systems with countably many transformations by showing the existence and extending earlier characterisations of the equilibrium states of finite…
We study infinite graph-directed iterated function systems (GIFS) whose underlying graph is not strongly connected and has countably many vertices and edges. In addition to a summability condition for the physical potential, we provide…
In this work we propose a definition of an Euroattractor: an attracting invariant measure of a certain iterated functions system (IFS). An IFS is defined by specifying a set of functions, defined in subsets of R^N or in a classical phase…
We consider the dimension and measure of typical attractors of random iterated function systems (RIFSs). We define a RIFS to be a finite set of (deterministic) iterated function systems (IFSs) acting on the same metric space and, for a…
In this article we introduce and investigate a new class of rearrangement invariant (r.i.) Banach function spaces, so-called Composed Grand Lebesgue Spaces (CGLS), in particular, Integral Grand Lebesgue Spaces (IGLS), which are some…
We construct a wavelet and a generalised Fourier basis with respect to some fractal measures given by one-dimensional iterated function systems. In this paper we will not assume that these systems are given by linear contractions…
In this paper we present some new results on the existence of solutions of generalized variational inequalities in real reflexive Banach spaces with Fr\'echet differentiable norms. Moreover, we also give some theorems about the structure of…
In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approximation. This result shows that for a family of limsup sets,…