\(\varphi\)-contractive parent-child possibly infinite IFSs and orbital \(\varphi\)-contractive possibly infinite IFSs. (English) Zbl 07884564
Summary: In this paper we introduce the notions of \(\varphi\)-contractive parent-child possibly infinite iterated function system (pcIIFS) and orbital \(\varphi\)-contractive possibly infinite iterated function system (oIIFS) and we prove that the corresponding fractal operator is weakly Picard. The corresponding notions of shift space, canonical projection and their properties are also treated.
MSC:
| 28A80 | Fractals |
| 37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |
| 37C25 | Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics |
Keywords:
weakly Picard operator; fractal operator; infinite iterated function system; canonical projectionReferences:
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