Conjugacy invariants of a $D_{\infty}$-Topological Markov chain

Time reversal symmetry arises in many dynamical systems. In particular, it is an important aspect of dynamical systems which emerge from physical theories such as classical mechanics, thermodynamics and quantum mechanics. In this talk, we introduce the notion of a reversible dynamical system in symbolic dynamics. We investigate conjugacy invariants of a topological Markov chain which possesses an involutory reversing symmetry.