| Popis: |
One of the most basic, longstanding open problems in the theory of dynamicalsystems is whether reachability is decidable for one-dimensional piecewiseaffine maps with two intervals. In this paper we prove that for injective maps,it is decidable. We also study various related problems, in each case eitherestablishing decidability, or showing that they are closely connected toDiophantine properties of certain transcendental numbers, analogous to thepositivity problem for linear recurrence sequences. Lastly, we considertopological properties of orbits of one-dimensional piecewise affine maps, notnecessarily with two intervals, and negatively answer a question of Bournez,Kurganskyy, and Potapov, about the set of orbits in expanding maps. |
