Reachability Problems in Low-Dimensional Iterative Maps


In this paper we analyse the dynamics of one-dimensional piecewise maps (PAMs). We show that one-dimensional PAMs are equivalent to pseudo-billiard or so called “strange billiard” systems. We also show that the more general class of rational functions leads to undecidability of reachability problem for one-dimensional piecewise maps with a finite number of intervals.


    20 Figures and Tables

    Download Full PDF Version (Non-Commercial Use)