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.

• Type: Journal
• Year: 2008
• Where: IJFCS
• Authors: Oleksiy Kurganskyy, Igor Potapov, Fernando Sancho-Caparrini
• Keywords: IJFCS 2008, One-dimensional Pams, One-dimensional Piecewise, Strange Billiard