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Notes on the Transversality Method for Iterated Function Systems—A Survey
Mathematical and Computational Applications, 2023 This is a brief survey of selected results obtained using the “transversality method” developed for studying parametrized families of fractal sets and measures. We mostly focus on the early development of the theory, restricting ourselves to self-similar
Boris Solomyak
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On the Attractor of One-Dimensional Infinite Iterated Function Systems [PDF]
, 2013 We study the attractor of Iterated Function Systems composed of infinitely many affine, homogeneous maps. In the special case of second generation IFS, defined herein, we conjecture that the attractor consists of a finite number of non-overlapping ...
Mantica, Giorgio
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ON RANDOM ITERATED FUNCTION SYSTEMS WITH GREYSCALE MAPS
Image Analysis and Stereology, 2012 In the theory of Iterated Function Systems (IFSs) it is known that one can find an IFS with greyscale maps (IFSM) to approximate any target signal or image with arbitrary precision, and a systematic approach for doing so was described.
Matthew Demers +2 more
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The structure of fuzzy fractals generated by an orbital fuzzy iterated function system
Demonstratio Mathematica, 2023 In this article, we present a structure result concerning fuzzy fractals generated by an orbital fuzzy iterated function system ((X,d),(fi)i∈I,(ρi)i∈I)\left(\left(X,d),{({f}_{i})}_{i\in I},{\left({\rho }_{i})}_{i\in I}). Our result involves the following
Savu Irina +2 more
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Equilibrium states of generalised singular value potentials and applications to affine iterated function systems [PDF]
, 2017 We completely describe the equilibrium states of a class of potentials over the full shift which includes Falconer’s singular value function for affine iterated function systems with invertible affinities.
J. Bochi, I. Morris
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Quantum Iterated Function Systems
, 2003 Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act randomly with ...
A. Lasota +48 more
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Attractors of iterated function systems and Markov operators
Abstract and Applied Analysis, 2003 This paper contains a review of results concerning generalized attractors for a large class of iterated function systems {wi:i∈I} acting on a complete separable metric space.
Józef Myjak, Tomasz Szarek
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Iterated function systems, representations, and Hilbert space
, 2004 This paper studies a general class of Iterated Function Systems (IFS). No contractivity assumptions are made, other than the existence of some compact attractor. The possibility of escape to infinity is considered.
Bratteli O. +4 more
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Topological pressures of a factor map for iterated function systems
AIMS MathematicsIn this manuscript, we mainly investigate the topological pressure for iterated function systems on a compact metric space defined by Wang and Liao [Dynam. Syst., 2021, 36(3): 483–506].
Zhongxuan Yang +2 more
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Arcwise connected attractors of infinite iterated function systems
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 The aim of this paper is to give a sufficient condition for the attractor of an infinite iterated function system to be arcwise connected.
Dumitru Dan
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