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Iterated Function Systems, Iterated Multifunction Systems, and Applications
, 2008 In the first part of the paper we recall the theory of iterated function systems and iterated multifunction systems. In the second part we show some applications in economics, statistics and finance.
C. Colapinto, D. La Torre
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Refinable functions, functionals, and iterated function systems
Applied Mathematics and Computation, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Francesco Calabrò +3 more
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From iterated function systems to iterated multifunction systems
, 2008 Starting from the original definitions of Iterated Function Systems (IFS) and Iterated Function Systems with Probabilities (IFSP) we introduce the notions of Iterated Multifunction Systems (IMS) and Iterated Multifunction Systems with Probabilities (IMSP).
H. Kunze, D. La Torre, E. R. Vrscay
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Chaos in Iterated Function Systems
International Journal of Bifurcation and Chaos, 2020In the present paper, we study chaos in iterated function systems (IFS), namely dynamical systems with several generators. We introduce weak Li–Yorke chaos, chaos in branch, and weak topological chaos to perceive the role of branches to create chaos in an IFS. Moreover, we define another type of chaos, [Formula: see text]-chaos, on an IFS.
Maliheh Mohtashamipour +1 more
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Fractals, 2010
In 1969, Kannan1 gave the definition of a new mapping which had presented a condition which is more lenient than contraction condition. The purpose of this note is to introduce K-Iterated Function System using Kannan mapping which will cover a larger range of mappings. We also prove the Collage theorem for the K-Iterated Function System.
Sahu, D. R. +2 more
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In 1969, Kannan1 gave the definition of a new mapping which had presented a condition which is more lenient than contraction condition. The purpose of this note is to introduce K-Iterated Function System using Kannan mapping which will cover a larger range of mappings. We also prove the Collage theorem for the K-Iterated Function System.
Sahu, D. R. +2 more
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Iterated function systems and dynamical systems
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1995We study the relationship between measures invariant for a piecewise expanding transformation τ of a compact metric space endowed with a underlying measure and measures invariant for an iterated function system Tτ, generated by inverse branches of τ. The main result says that the τ-invariant absolutely continuous measure μ is also Tτ invariant if and ...
Góra, Paweł, Boyarsky, Abraham
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, 2007 Diplomdarbā ir parādīts, kā ar iteratīvu funkciju sistēmu palīdzību var izveidot fraktāļus. Iteratīvo funkciju sistēmas tiek veidotas no saspiedējattēlojumiem.
Vasiļjeva, Kira
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Infinite Iterated Function Systems
Mathematische Nachrichten, 1994AbstractWe examine iterated function systems consisting of a countably infinite number of contracting mappings (IIFS). We state results analogous to the well‐known case of finitely many mappings (IFS). Moreover, we show that IIFS can be approximated by appropriately chosen IFS both in terms of Hausdorff distance and of Hausdorff dimension.
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ITERATED FUNCTION SYSTEMS ON FUNCTIONS OF BOUNDED VARIATION
Fractals, 2016We show that under certain hypotheses, an iterated function system on mappings (IFSM) is a contraction on the complete space of functions of bounded variation (BV). It then possesses a unique attractor of BV. Some BV-based inverse problems based on the Collage Theorem for contraction maps are considered.
D. La Torre, F. Mendivil, E. R. Vrscay
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Iterated Function Systems, Capacity and Green’s Functions
Computational Methods and Function Theory, 2004The iterated function system \(f_1, \ldots, f_m: \mathbb C\to\mathbb C\) with Lipschitz bounds \[ a_j | z-w| \leq | f_j(z)-f_j(w)| \leq b_j | z-w| , \] for ...
Baribeau, Line +3 more
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