Related papers: Understanding the limit sets generated by general …
In this paper, we study the Hausdorff dimension of self-similar measures and sets on the real line, where the generating iterated function system consists of some maps that share the same fixed point. In particular, we will show that out of…
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
Non-autonomous iterated function systems are a generalization of iterated function systems. If the contractions in the system are conformal mappings, it is called a non-autonomous conformal iterated function system, and its attractor is…
We show that for a transcendental entire function the set of points whose orbit under iteration is bounded can have arbitrarily small positive Hausdorff dimension.
In this paper we introduce the concept of infinite pointwise dense lineability (spaceability), and provide a criterion to obtain density from mere lineability. As an application, we study the linear and topological structures within the set…
It is known that Iterated Function Systems generated by orientation preserving homeomorphisms of the unit interval admit a unique invariant measure on $(0,1)$. The setup for this result is the positivity of Lyapunov exponents at both fixed…
The aim of the present paper is twofold. We study directed porosity in connection with conformal iterated function systems (CIFS) and with singular integrals. We prove that limit sets of finite CIFS are porous in a stronger sense than…
In dynamical systems, shrinking target sets and pointwise recurrent sets are two important classes of dynamically defined subsets. In this article we introduce a mild condition on the linear parts of the affine mappings that allow us to…
Generalization error bounds are critical to understanding the performance of machine learning models. In this work, building upon a new bound of the expected value of an arbitrary function of the population and empirical risk of a learning…
Orbit-finite sets are a generalisation of finite sets, and as such support many operations allowed for finite sets, such as pairing, quotienting, or taking subsets. However, they do not support function spaces, i.e. if X and Y are…
In this paper, we study the existence of fixed points for mappings defined on complete (compact) metric space (X, d) satisfying a general contractive (contraction) inequality depended on another function. These conditions are analogous to…
In this paper, using the monotone iterative technique and the Banach contraction mapping principle, we study a class of fractional differential system with integral boundary on an infinite interval. Some explicit monotone iterative schemes…
We examine how implicit functions on ILB-Fr\'echet spaces can be obtained without metric or norm estimates which are classically assumed. We obtain implicit functions defined on a domain $D$ which is not necessarily open, but which contains…
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
We introduce a harmonic analysis for a class of affine iteration models in $\br^d$. Using Hilbert-space geometry, we develop a new duality notion for affine and contractive iterated function systems (IFSs) and we construct some identities…
We define iteration of functions that map n-dimensional vector spaces into m-dimensional vector spaces (m at most equal to n). It happens that usual iteration and Fibonacci iterative methods become special cases of this generalized…
We develop a methodology to learn finitely generated random iterated function systems from time-series of partial observations using delay embeddings. We obtain a minimal model representation for the observed dynamics, using a hidden…
A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new even for isometries of Banach spaces as well as for non-locally compact…
The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional…
We propose a method to obtain iterative schemes guarantee unique solutions for systems of partial differential equations that are not symmetric with respect to the time by generalizing He variational iteration method and using Banach fixed…