Abstract
A continuous map f from a metric space X to itself is said to contain a two-sided symbolic dynamical system if there exists an invariant set X0 of f such that the subsystem f|X0 is topologically conjugate to the shift map on a two-sided sequence space of some symbols. In this paper we show that, for any given integer n ≥ 2, there exists a Lipschitz continuous interval map which contains a two-sided symbolic dynamical system of n symbols. Furthermore, we investigate the effect of differentiability and monotonicity assumptions, and prove that neither piecewise monotonic nor piecewise continuously differentiable graph map can contain a two-sided symbolic dynamical system.
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