The existence of the attractor of countable iterated function systems
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Publication:414385
DOI10.1007/S00009-011-0116-XzbMath1242.28014OpenAlexW2011744194MaRDI QIDQ414385
Publication date: 11 May 2012
Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00009-011-0116-x
Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Fractals (28A80) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25)
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Approximating the attractor set of countable iterated function systems by \(\alpha\)-dense curves ⋮ Local Countable Iterated Function Systems ⋮ Fractional calculus on fractal interpolation for a sequence of data with countable iterated function system ⋮ New equilibria of non-autonomous discrete dynamical systems ⋮ Generalized \(F\)-iterated function systems on product of metric spaces ⋮ Non-stationary \(\phi\)-contractions and associated fractals ⋮ Iterated function systems consisting of \(F\)-contractions ⋮ New type of fractal functions for the general data sets ⋮ Semifractals from multifunctions on product spaces and generalized iterated function systems ⋮ Interpolative operators: fractal to multivalued fractal ⋮ Bernstein super fractal interpolation function for countable data systems ⋮ Countable contraction mappings in metric spaces: invariant sets and measure ⋮ Invariant measure associated with a generalized countable iterated function system ⋮ Countable zipper fractal interpolation and some elementary aspects of the associated nonlinear zipper fractal operator ⋮ Dendrite-type attractors of infinite iterated function systems ⋮ Iterated function systems consisting of \(\varphi \)-contractions ⋮ Separation properties of \((n,m)\)-IFS attractors ⋮ Topological version of generalized (infinite) iterated function systems ⋮ Fractal approximation of a function from a countable sample set and associated fractal operator ⋮ Contractive iterated function systems enriched with nonexpansive maps ⋮ Cyclic iterated function systems ⋮ Cyclic Meir-Keeler Contraction and Its Fractals ⋮ Existence of a fractal of iterated function systems containing condensing functions for the degree of nondensifiability ⋮ Cyclic weak \(\phi\) iterated function system
Cites Work
- Iterated function systems and well-posedness
- Applications of fixed point theorems in the theory of generalized IFS
- A generalization of IFS with probabilities to infinitely many maps
- A generalization of the Hutchinson measure
- A theorem on contraction mappings
- A lattice-theoretical fixpoint theorem and its applications
- Generalized iterated function systems, multifunctions and Cantor sets
- On Fixed and Periodic Points Under Contractive Mappings
- Infinite Iterated Function Systems
- On natural invariant measures on generalised iterated function systems
- Lipscomb's space $\omega^{A}$ is the attractor of an infinite IFS containing affine transformations of $l^{2}(A)$
- The Hutchinson-Barnsley theory for infinite iterated function systems
- Infinite Iterated Function Systems: A Multivalued Approach
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