MICRO AND MACRO FRACTALS GENERATED BY MULTI-VALUED DYNAMICAL SYSTEMS

@inproceedings{Banakh2014MICROAM,
  title={MICRO AND MACRO FRACTALS GENERATED BY MULTI-VALUED DYNAMICAL SYSTEMS},
  author={Taras O. Banakh and Natalia Novosad},
  year={2014}
}
Given a multi-valued function Φ : X ⊸ X on a topological space X we study the properties of its fixed fractal, which is defined as the closure of the orbit Φω(*Φ) = ⋃n∈ωΦn(*Φ) of the set *Φ = {x ∈ X : x ∈ Φ(x)} of fixed points of Φ. A special attention is paid to the duality between micro-fractals and macro-fractals, which are fixed fractals and for a contracting compact-valued function Φ : X ⊸ X on a complete metric space X. With help of algorithms (described in this paper) we generate various… CONTINUE READING
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