Topological Conjugacy and Symbolic dynamics of the one dimensional map - Biswas, Hena (European Journal of Applied Sciences, 2021)
In the study of nonlinear physical systems, one encounters possibly random or chaotic behavior, although the techniques may be perfectly deterministic. Topological conjugacy is essential in the study of iterated functions and, more generally, dynamical systems. Our goal is to show that conjugacy (topological) and symbolic dynamics are a distinguished combination of tools of dynamical systems. This paper investigates conjugacy between different one-dimensional maps and discusses semi-conjugacy between doubling maps and shift maps. Finally, we discuss employing techniques from symbolic dynamics to one-dimensional maps, which means how extended dynamics work for one dimensional map.