Topological Horseshoes and Coin-Tossing Dynamics

Lakshmi Burra ()
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Lakshmi Burra: Jawaharlal Nehru Technological University, Department of Mathematics

Chapter Chapter 2 in Chaotic Dynamics in Nonlinear Theory, 2014, pp 29-53 from Springer

Abstract: 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.

Keywords: Coin-tossing; Semi-conjugacy; Bernoulli shift; Stretching along paths. (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-2092-3_2

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DOI: 10.1007/978-81-322-2092-3_2

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