Results 131 to 140 of about 153,517 (179)
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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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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, Iterated Multifunction Systems, and Applications
2008In 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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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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Chaotic iterated function systems
Archiv der Mathematik, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Cyclic iterated function systems
Journal of Fixed Point Theory and Applications, 2020The existence of an unique fixed point of the Hutchinson operator for three IFS (iterated function system) is proved: generated by cyclic contractions, cyclic \(\varphi\)-contractions (see [\textit{W. A. Kirk} et al., Fixed Point Theory 4, No. 1, 79--89 (2003; Zbl 1052.54032)]) and by cyclic (c)-comparison maps [\textit{V.
R. Pasupathi +2 more
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Parabolic iterated function systems
Ergodic Theory and Dynamical Systems, 2000In this paper we introduce and explore conformal parabolic iterated function systems. We define and study topological pressure, Perron–Frobenius-type operators, semiconformal and conformal measures and the Hausdorff dimension of the limit set. With every parabolic system we associate an infinite hyperbolic conformal iterated function system and we ...
Mauldin, R. D., Urbański, M.
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Random iteration for infinite nonexpansive iterated function systems
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015We prove that the random iteration algorithm works for strict attractors of infinite iterated function systems. The system is assumed to be compactly branching and nonexpansive. The orbit recovering an attractor is generated by a deterministic process and the algorithm is always convergent.
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2009
In the early 1980's, Michael Barnsley introduced the idea of synthesizing a predetermined image as the attractor of a chaotic process. Other researchers had previously shown that chaotic systems were capable of producing fascinating images known as strange attractors.
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In the early 1980's, Michael Barnsley introduced the idea of synthesizing a predetermined image as the attractor of a chaotic process. Other researchers had previously shown that chaotic systems were capable of producing fascinating images known as strange attractors.
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Iterated Functions Systems Music
Computer Music Journal, 1991As a new technique of computer-assisted composition, measures of attractors of iterated functions systems codes (Barnsley 1989) can be interpreted as musical scores. The technique is called here "IFS music." In some important respects, it appears to be more general and more powerful than previous methods for generating musical scores from fractals ...
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