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Topological Horseshoes and Coin-Tossing Dynamics

In: Chaotic Dynamics in Nonlinear Theory

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  • Lakshmi Burra

    (Jawaharlal Nehru Technological University, Department of Mathematics)

Abstract

In the previous chapter, various prevalent definitions of chaotic dynamics were given. In this chapter, the notion in which we use chaos is explained. Amongst the many definitions of chaos which are used in literature, we choose the definition of chaos which is related to “stretching along paths”. We show how the method of “stretching along paths”, is used to prove the presence of chaotic dynamics in dynamical systems. The definition of chaos that we choose is adapted from the one considered by Kirchgraber and Stoffer [1] under the name of chaos in the coin-tossing sense. In fact, exactly like in [1], our definition concerns the possibility of reproducing, via the iterates of a given map $$\psi $$ ψ any coin-flipping sequence of two symbols.

Suggested Citation

  • Lakshmi Burra, 2014. "Topological Horseshoes and Coin-Tossing Dynamics," Springer Books, in: Chaotic Dynamics in Nonlinear Theory, edition 127, chapter 0, pages 29-53, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-2092-3_2
    DOI: 10.1007/978-81-322-2092-3_2
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