17 citations · 52 across the 20 of their papers we have counts for
22 papers
On the equicontinuity of the Hutchinson operator
Filip Strobin, Piotr Szuca
We show that the Hutchinson operator of an Iterated Function System with an attractor is equicontinuous if and only if it is continuous; in particular, every finite Iterated Functi…
A topological approach to fuzzy iterated function systems
Taras Banakh, Krzysztof Caban, Filip Strobin
In the paper we unify two extensions of the classical Hutchinson--Barnsley theory - the topological and the fuzzy-set approaches. We show that a fuzzy iterated function system (fuz…
Strongly-Fibred Iterated Function Systems and the Barnsley--Vince triangle
Krzysztof Leśniak, Nina Snigireva, Filip Strobin
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 pr…
Transition Phenomena for the Attractor of an Iterated Function System
Krzysztof Leśniak, Nina Snigireva, Filip Strobin +1
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 h…
Fuzzy-set approach to invariant idempotent measures
Rudnei D. da Cunha, Elismar R. Oliveira, Filip Strobin
We provide a new approach to the Hutchinson-Barnsley theory for idempotent measures first presented in N. Mazurenko, M. Zarichnyi, Invariant idempotent measures, Carpathian Math. P…
Existence of invariant idempotent measures by contractivity of idempotent Markov operators
Rudnei D. da Cunha, Elismar R. Oliveira, Filip Strobin
We prove that the idempotent Markov operator generated by contractive max plus normalized iterated function system (IFS) is also a contractive map w.r.t. natural metrics on the spa…