Search results for "Hutchinson operator"

showing 3 items of 3 documents

Generalized iterated function systems on the spacel∞(X)

2014

Abstract In the last decades there has been a current effort to extend the classical Hutchinson theory of iterated function systems composed by contractions on a metric space X into itself to more general spaces and infinitely many mappings. In this paper we consider the (countable) iterated function systems consisting of some generalized contractions on the product space X I into X , where I is an arbitrary set of natural numbers. Some approximations of the attractors of the respective iterated function systems are given.

Discrete mathematicsHutchinson operatorMetric spaceIterated function systemCollage theoremApplied MathematicsCountable setContraction mappingTopological conjugacySpace (mathematics)AnalysisMathematicsJournal of Mathematical Analysis and Applications
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Generalized countable iterated function systems

2011

One of the most common and most general way to generate fractals is by using iterated function systems which consists of a finite or infinitely many maps. Generalized countable iterated function systems (GCIFS) are a generalization of countable iterated function systems by considering contractions from X ? X into X instead of contractions on the metric space X to itself, where (X, d) is a compact metric space. If all contractions of a GCIFS are Lipschitz with respect to a parameter and the supremum of the Lipschitz constants is finite, then the associated attractor depends continuously on the respective parameter.

Hutchinson operatorDiscrete mathematicsMetric spaceIterated function systemCollage theoremGeneral MathematicsCountable setContraction mappingLipschitz continuityCosmic spaceMathematicsFilomat
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Iterated function systems and well-posedness

2009

Abstract Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems in several topics of applied sciences [see for example: El Naschie MS. Iterated function systems and the two-slit experiment of quantum mechanics. Chaos, Solitons & Fractals 1994;4:1965–8; Iovane G. Cantorian spacetime and Hilbert space: Part I-Foundations. Chaos, Solitons & Fractals 2006;28:857–78; Iovane G. Cantorian space-time and Hilbert space: Part II-Relevant consequences. Chaos, Solitons & Fractals 2006;29:1–22;…

Hutchinson operatorDiscrete mathematicsPure mathematicsSpacetimeDynamical systems theoryGeneral MathematicsApplied MathematicsHilbert spaceGeneral Physics and AstronomyStatistical and Nonlinear PhysicsMetric spacesymbols.namesakeIterated function systemIterated functionsymbolsUniquenessMathematicsChaos, Solitons & Fractals
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