Borel complexity of the family of attractors for weak IFSs
Sign Up to like & getrecommendations! Published in 2022 at "Acta Mathematica Hungarica"
DOI: 10.1007/s10474-021-01199-7
Abstract: This paper is an attempt to measure the difference between the family of iterated function systems attractors and a broader family, the set of attractors for weak iterated function systems. We discuss Borel complexity of… read more here.
Keywords: function systems; borel complexity; attractors weak; iterated function ... See more keywords
The canonical projection associated with certain possibly infinite generalized iterated function systems as a fixed point
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Fixed Point Theory and Applications"
DOI: 10.1007/s11784-018-0618-2
Abstract: In this paper, influenced by the ideas from Mihail (Fixed Point Theory Appl 2015:15, 2015), we associate to every generalized iterated function system $$\mathcal {F}$$F (of order m) an operator $$H_{\mathcal {F}}:\mathcal {C} ^{m}\rightarrow \mathcal… read more here.
Keywords: fixed point; iterated function; projection associated; canonical projection ... See more keywords
Hardy–Rogers Type Iterated Function Systems
Sign Up to like & getrecommendations! Published in 2020 at "Qualitative Theory of Dynamical Systems"
DOI: 10.1007/s12346-020-00378-1
Abstract: In this paper we introduce the concept of Hardy–Rogers type iterated function system and we prove that the fractal operator associated to such a system is a Picard operator. Some examples are provided. read more here.
Keywords: systems hardy; type iterated; rogers type; iterated function ... See more keywords
The Asymptotic Average Shadowing Property of Iterated Function Systems
Sign Up to like & getrecommendations! Published in 2021 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-021-01184-x
Abstract: In this paper, we explore the asymptotic average shadowing property of iterated function systems. We show that for an iterated function system IFS $$(\mathscr {F})$$ such that one of $$\mathscr {F}$$ is surjective, the pseudo-orbital… read more here.
Keywords: average shadowing; iterated function; shadowing property; asymptotic average ... See more keywords
A strongly irreducible affine iterated function system with two invariant measures of maximal dimension
Sign Up to like & getrecommendations! Published in 2020 at "Ergodic Theory and Dynamical Systems"
DOI: 10.1017/etds.2020.107
Abstract: Abstract A classical theorem of Hutchinson asserts that if an iterated function system acts on $\mathbb {R}^{d}$ by similitudes and satisfies the open set condition then it admits a unique self-similar measure with Hausdorff dimension… read more here.
Keywords: measures maximal; dimension; iterated function; invariant measures ... See more keywords
Dimension estimates for iterated function systems and repellers. Part II
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DOI: 10.1017/etds.2021.92
Abstract: This is the second part of our study on the dimension theory of $C^1$ iterated function systems (IFSs) and repellers on $\mathbb {R}^d$ . In the first part [D.-J. Feng and K. Simon. Dimension estimates… read more here.
Keywords: function systems; dimension; part; iterated function ... See more keywords
Exponential control of the trajectories of iterated function systems with application to semi-strong GARCH models
Sign Up to like & getrecommendations! Published in 2023 at "Journal of Applied Probability"
DOI: 10.1017/jpr.2023.13
Abstract: We establish new results on the strictly stationary solution to an iterated function system. When the driving sequence is stationary and ergodic, though not independent, the strictly stationary solution may admit no moment but we… read more here.
Keywords: control trajectories; garch models; iterated function; exponential control ... See more keywords
The structure of fuzzy fractals generated by an orbital fuzzy iterated function system
Sign Up to like & getrecommendations! Published in 2023 at "Demonstratio Mathematica"
DOI: 10.1515/dema-2022-0217
Abstract: Abstract In this article, we present a structure result concerning fuzzy fractals generated by an orbital fuzzy iterated function system ( ( X , d ) , ( f i ) i ∈ I ,… read more here.
Keywords: function; function system; fuzzy fractals; iterated function ... See more keywords
Existence Results for Wardoski-Type Convex Contractions and the Theory of Iterated Function Systems
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DOI: 10.3390/sym15061162
Abstract: The purpose of this paper is to define the notion of extended convex F contraction by imposing less conditions on the function F satisfying certain contractive conditions. We prove the existence of fixed points for… read more here.
Keywords: function systems; results wardoski; existence results; iterated function ... See more keywords