Related papers: Diameter Diminishing To Zero IFSs
In this paper we introduce expansive iterated function systems, ( IFS) on a compact metric space then various shadowing properties and their equivalence are considered for expansive IFS.
In this paper, we introduce and investigate the notions of Mean Dimension and Metric Mean Dimension for generalized iterated function systems (IFS). We establish basic properties of these invariants and prove that Mean Dimension is always…
We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…
We study the minimality of almost every orbital branch of minimal iterated function systems (IFSs). We prove that this kind of minimality holds for forward and backward minimal IFSs generated by orientation-preserving homeomorphisms of the…
The dimension spectrum of a conformal iterated function system (CIFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. This brief note provides two constructions -- (i) a compact perfect set that cannot be…
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…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
We review some recent results on finite dimensional spin glasses by studying recent numerical simulations and their relationship with experiments. In particular we will show results obtained at zero and non zero temperature, focusing in the…
A new approach to disintegration of measures is presented, allowing one to drop the usually taken separability assumption. The main tool is a result on fibers in the spectrum of algebra of essentially bounded functions established recently…
Let $(X,d)$ be a compact metric space, and let an iterated function system (IFS) be given on $X$, i.e., a finite set of continuous maps $\sigma_{i}$: $ X\to X$, $i=0,1,..., N-1$. The maps $\sigma_{i}$ transform the measures $\mu $ on $X$…
We consider the minimization problem of the functional given by the sum of the fractional perimeter and a general Riesz potential, which is one generalization of Gamow's liquid drop model. We first show the existence of minimizers for any…
Continuous conformal transformation minimizes the conformal energy. The convergence of minimizing discrete conformal energy when the discrete mesh size tends to zero is an open problem. This paper addresses this problem via a careful error…
Subtractive dithered quantizers are examined to minimize the signal-band dither power. The design of finite impulse response(FIR) filters that shape most of the dither-power out of the signal band while maintaining the benefits of dithering…
In this work, we propose a self-consistent minimization procedure for functionals in reduced density matrix functional theory. We introduce an effective noninteracting system at finite temperature which is capable of reproducing the…
Several important conjectures in Fractal Geometry can be summarised as follows: If the dimension of a self-similar measure in $\mathbb{R}$ does not equal its expected value, then the underlying iterated function system contains an exact…
The aim of an invisibility device is to guide light around any object put inside, being able to hide objects from sight. In this work, we propose a novel design of dielectric invisibility media based on negative refraction and optical…
We present a new method to compare the shapes of genus-zero surfaces. We introduce a measure of mutual stretching, the symmetric distortion energy, and establish the existence of a conformal diffeomorphism between any two genus-zero…
What is a diffusion model actually doing when it turns noise into a photograph? We show that the deterministic DDIM reverse chain operates as a Partitioned Iterated Function System (PIFS) and that this framework serves as a unified design…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
In 1996, Strichartz introduced reverse iterated function systems (RIFS) $\mathcal{F}=\{f_i(x)=r_i x+b_i\}_{i=1}^m$ of expanding mappings on $\mathbb{Z}$ and left the determination of the general dimension formulas of invariant sets as an…