TY  - JOUR
ID  - Guzik2025
LB  - Guzik2025
AU  - Guzik, Grzegorz
AU  - Kleszcz, Grzegorz
TI  - From set-valued dynamical processes to fractals
ST  - From set-valued dynamical processes to fractals
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2025
VL  - 45
IS  - 5
SP  - 601
EP  - 621
DO  - https://doi.org/10.7494/OpMath.2025.45.5.601
UR  - https://doi.org/10.7494/OpMath.2025.45.5.601
AB  - We present a general theory of topological semiattractors and attractors for set-valued semigroups. Our results extend and unify those previously obtained by Lasota and Myjak. In particular, we naturally generalize the concept of semifractals for the systems acting on Hausdorff topological spaces. The main tool in our analysis is the notion of topological (Kuratowski) limits. We especially focus on the forward asymptotic behavior of discrete set-valued processes generated by sequences of iterated function systems. In this context, we establish sufficient conditions for the existence of fractal-type limit sets.
KW  - topological limit
KW  - lower semicontinuous multifunction
KW  - iterated function system
KW  - set-valued process
KW  - attractor
SN  - 1232-9274
ER  -