On the dynamics of the Tent function-Phase diagrams

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Modem Science Publishers
This paper focuses on the study of a one dimensional topological dynamical system, the tent function. We give a good background to the theory of dynamical systems while establishing the important asymptotic properties of topological dynamical systems that distinguishes it from other fields by way of an example - the tent function. A precise definition of the tent function is given and iterates are clearly shown using the phase diagrams. By this same method, chaos in the tent map is shown as iterates become higher. We also show that the tent map has infinitely many chaotic orbits and also express some important features of chaos such as topological transitivity, boundedness and sensitivity to change in initial conditions from a topological viewpoint.
This article is published by Modem Science Publishers and is also available at http://dx.doi.org/10.20454/jast.2016.1011
Journal of Advanced Studies in Topology 7:4 (2016), 261–270