Block-Coppels chaos in set-valued discrete systems

Document Type : Research Article

Authors

Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.

Abstract

Let (X, d) be a compact metric space and f : X → X be a continuous map. Consider the metric space (K(X), H) of all non empty compact subsets of X endowed with the Hausdorff metric induced by d. Let ¯f : K(X) → K(X) be defined by ¯f (A) =
{f (a) : a ∈ A} . We show that Block-Coppels chaos in f implies Block-Coppels chaos in ¯f if f is a bijection.

Keywords

References

1. Gu, R. and Guo, W., On mixing property in set- valued discrete systems. Chaos, Solitons & Fractals, 28, (2006), 747-754.
2. Gu, R., Katos chaos in set-valued discrete systems. Chaos, Solitons & Fractals, 31, (2007), 765-771.
3. Palmisani, Ch., Chaotic Dynamics in Solow-type Growth Models. Doctoral thesis, University of Naples Federico II, (2008).
4. Roman-Flores, H., A note on transitivity in set-valued discrete systems. Chaos, Solitons & Fractals, 17, (2003), 99104.
5. Roman-Flores, H. and Chalco-Cano Y., Robinsons chaos in set-valued discrete systems. Chaos, Solitons & Fractals, 25, (2005), 33-42.
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