A COUNTEREXAMPLE TO ELAYDI’S CONJECTURE

Abstract

In this work, we define a chaotic map that contradicts Elaydi’s conjecture. Firstly, we present some important concepts used in this paper and define a continuous map f on [0,2], which is connected according to the usual topology on R. Moreover, we show that f is chaotic on [0,2] by using topological conjugacy with the ‘tent map’. Finally, we conclude that f^2=f∘f is not chaotic on [0,2]. In addition, this example also shows that topological transitivity does not imply total transitivity.

Keywords

• Chaos
• Topologically Transitive
• Totally Transitive
• Topological Conjugacy

References

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