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Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated function system (IFS) corresponding to the data set is the graph of the FIF. Coalescence…

Dynamical Systems · Mathematics 2015-09-08 Md. Nasim Akhtar , M. Guru Prem Prasad

In this paper we present a systematic study of continuous local iterated function systems. We prove local iterated function systems admit compact attractors and, under a contractivity assumption, construct their code space and present an…

Dynamical Systems · Mathematics 2026-01-13 Elismar R. Oliveira , Paulo Varandas

We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function…

Dynamical Systems · Mathematics 2017-11-01 Katrin Gelfert , Örjan Stenflo

This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function…

Dynamical Systems · Mathematics 2009-11-13 Mario Roy , Hiroki Sumi , Mariusz Urbanski

In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…

Statistics Theory · Mathematics 2007-06-13 Stefano M. Iacus , Davide La Torre

In this paper, we study cut sets of attractors of iteration function systems (IFS) in $\mathbb{R}^d$. Under natural conditions, we show that all irreducible cut sets of these attractors are perfect sets or single points. This leads to a…

General Topology · Mathematics 2014-12-08 Benoît Loridant , Jun Luo , Tarek Sellami , Jörg Thuswaldner

We study the moments of equilibrium measures for iterated function systems (IFSs) and draw connections to operator theory. Our main object of study is the infinite matrix which encodes all the moment data of a Borel measure on R^d or C. To…

Classical Analysis and ODEs · Mathematics 2011-12-15 Palle Jorgensen , Keri Kornelson , Karen Shuman

In this work we present iterated function systems with general measures(IFSm) formed by a set of maps $\tau_{\lambda}$ acting over a compact space $X$, for a compact space of indices, $\Lambda$. The Markov process $Z_k$ associated to the…

Dynamical Systems · Mathematics 2025-05-15 Elismar R. Oliveira , Rafael R. Souza

We investigate iterated function systems (IFS) that randomly alternate between two non-identical one-dimensional maps. Our primary focus is on finite invariant sets exhibiting ``toss-and-catch'' dynamics, in which trajectories alternate…

Dynamical Systems · Mathematics 2026-04-16 Hibiki Kato , Tamotsu Onozaki , Yoshitaka Saiki , Yasumasa Sugita

This preliminary paper presents initial explorations in rendering Iterated Function System (IFS) fractals using a differentiable rendering pipeline. Differentiable rendering is a recent innovation at the intersection of computer graphics…

Graphics · Computer Science 2024-06-11 Cory Braker Scott

Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem…

Numerical Analysis · Mathematics 2018-10-26 Antonio Cicone , Haomin Zhou

We study new relations between countable iterated function systems (IFS) with overlaps, Smale endomorphisms and random systems with complete connections. We prove that stationary measures for countable conformal IFS with overlaps and…

Dynamical Systems · Mathematics 2022-02-16 Eugen Mihailescu , Mariusz Urbanski

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 $X$…

Classical Analysis and ODEs · Mathematics 2007-05-23 Palle E. T. Jorgensen

In the analysis of real-world data, extracting meaningful features from signals is a crucial task. This is particularly challenging when signals contain non-stationary frequency components. The Iterative Filtering (IF) method has proven to…

Numerical Analysis · Mathematics 2026-04-01 Giuseppe Scarlato , Antonio Cicone , Marco Donatelli

In this paper, we focus attention on extending the topological conjugacy of adding machine maps and minimal systems to iterated function systems. We provide necessary and sufficient conditions for an iterated function system to be…

Dynamical Systems · Mathematics 2016-12-20 Mehdi Fatehi Nia

This paper discusses, certain algebraic, analytic, and topological results on partial iterated function systems($IFS_p$'s). Also, the article proves the Collage theorem for partial iterated function systems. Further, it provides a method to…

Dynamical Systems · Mathematics 2022-12-09 Praveen M , Sunil Mathew

The aim of this paper is to establish some results regarding Infinite Iterated Function Systems with the help of the Tarski-Kantorovitch fixed-point principles for maps on partially ordered sets. To this end we introduce two new classes of…

Dynamical Systems · Mathematics 2021-10-12 Bogdan-Alexandru Luchian

The present work is concerned with the eqiucontinuity and sensitivity of iterated function systems (IFSs). Here, we consider more general case of IFSs, i.e. the IFSs generated by a family of relations. We generalize the concepts of…

Dynamical Systems · Mathematics 2019-05-21 F. H. Ghane , E. Rezaali , A. Sarizadeh

We recast the notion of parablender introduced in [Berger2015] as a parametric IFS. This is done using the concept of open covering property and looking to parametric IFS as systems acting on jets.

Dynamical Systems · Mathematics 2016-05-31 Pierre Berger , Sylvain Crovisier , Enrique Pujals

A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…

Mathematical Physics · Physics 2014-10-16 R. Aldrovandi