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- Michael F. Barnsley, Krzysztof Lesniak
- I. J. Bifurcation and Chaos
- 2014

We investigate combinatorial issues relating to the use of random orbit approximations to the attractor of an iterated function system with the aim of clarifying the role of the stochastic process during generation the orbit. A Baire category counterpart of almost sure convergence is presented; and a link between topological and probabilistic methods is… (More)

- Michael F. Barnsley, Krzysztof Lesniak
- Symmetry
- 2015

We investigate when the Hutchinson operator associated with an iterated function system is continuous. The continuity with respect to both the Hausdorff metric and Vietoris topology is carefully considered. An example showing that the Hutchinson operator on the hyperspace of nonempty closed bounded sets need not be Hausdorff continuous is given. Infinite… (More)

- Krzysztof Lesniak
- ArXiv
- 2013

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 comparison of the Prisoner’s Dilemma with the Traveler’s Dilemma. They are also resistant on the deep… (More)

We fill the gap in understanding the relationship between mappings which are condensing w.r.t. the measure of noncompactness defined on the hyperspace and multifunctions condensing in the ordinary sense.

- Krzysztof Lesniak
- Chaos
- 2015

We 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. We also formulate a version of the random iteration for uncountable… (More)

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