Pattern avoidance in dynamical systems

摘要: Orbits generated by discrete-time dynamical systems have some interesting combinatorial properties. In this paper we address the existence of forbidden order patterns when dynamics is piecewise monotone maps on one-dimensional closed intervals. This means that points belonging to a sufficiently long orbit cannot appear in any arbitrary order. The admissible are then (the inverses of) those permutations avoiding so-called root consecutive positions. last part studies and enumerates shift systems, which universal models information theory, stochastic processes. spite their simple structure, exhibit all important features low-dimensional chaos, allowing export results other via order-isomorphisms. summarizes from [1] [11].