Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Lesniak, Krzysztof"'
We review the theory of semiattractors associated with non-contractive Iterated Function Systems (IFSs) and demonstrate its applications on a concrete example. In particular, we present criteria for the existence of semiattractors due to Lasota and M
Externí odkaz:
http://arxiv.org/abs/2209.04667
Autor:
Leśniak, Krzysztof, Nowak, Magdalena
Publikováno v:
Banach Center Publ. 125 (2023) 71-80
We define two non-metrizable compact spaces and show that they are attractors of iterated function systems. Both of them, the split square and the split carpet, are constructed using the product of split intervals.
Comment: 7 pages, 2 figures
Comment: 7 pages, 2 figures
Externí odkaz:
http://arxiv.org/abs/2208.14253
Iterated function systems (IFSs) and their attractors have been central to the theory of fractal geometry almost from its inception. And contractivity of the functions in the IFS has been central to the theory of iterated functions systems. If the fu
Externí odkaz:
http://arxiv.org/abs/2205.01185
We give a systematic account of iterated function systems (IFS) of weak contractions of different types (Browder, Rakotch, topological). We show that the existence of attractors and asymptotically stable invariant measures, and the validity of the ra
Externí odkaz:
http://arxiv.org/abs/2004.11057
Akademický článek
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Akademický článek
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We explore the chaos game for the continuous IFSs on topological spaces. We prove that the existence of attractor allows us to use the chaos game for visualization of attractor. The essential role of basin of attraction is also discussed.
Externí odkaz:
http://arxiv.org/abs/1410.3962
We define fractal continuations and the fast basin of the IFS and investigate which properties they inherit from the attractor. Some illustrated examples are provided.
Externí odkaz:
http://arxiv.org/abs/1308.4230
Autor:
Leśniak, Krzysztof
We show that under suitable conditions a random orbit generated by a system of nonexpansive maps recovers an invariant set via its omega-limit. In particular, this explains what happens to the Kaczmarz--von Neumann projection algorithm in the infeasi
Externí odkaz:
http://arxiv.org/abs/1307.5920
Autor:
Leśniak, Krzysztof
We investigate an alternative concept of Nash equilibrium, m-equilibrium, which slightly resembles Harsanyi-Selten risk dominant equilibrium although it is a different notion. M-equilibria provide nontrivial solutions of normal form games as shown by
Externí odkaz:
http://arxiv.org/abs/1306.6278