Symbolic Dynamics and Unpredictability Defined by Right Adjointness
Ralph L. Wojtowicz · AIP conference proceedings · 2004
It is shown that a category‐theoretic definition of chaotic system applies not only to the Smale horseshoe, a prototypical example, but also to Conway’s “Life.” Symbolic dynamics of the “Dining Philosophers” relational system is computed. A category composed of stochastic matrices is defined and its elementary properties are studied. A categorical variant of symbolic dynamics is applied to a finite stochastic process. Using point‐wise Kan extension formulas, conditions ensuring existence of certain representations between categories of dynamic systems are proved.