Reachability Problems for PAMs



Kurganskyy, Oleksiy and Potapov, Igor
(2016) Reachability Problems for PAMs. .

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Abstract

Piecewise affine maps (PAMs) are frequently used as a reference model to show the openness of the reachability questions in other systems. The reachability problem for one-dimensional PAM is still open even if we define it with only two intervals. As the main contribution of this paper we introduce new techniques for solving reachability problems based on p-adic norms and weights as well as showing decidability for two classes of maps. Then we show the connections between topological properties for PAM’s orbits, reachability problems and representation of numbers in a rational base system. Finally we show a particular instance where the uniform distribution of the original orbit may not remain uniform or even dense after making regular shifts and taking a fractional part in that sequence.

Item Type: Conference or Workshop Item (Unspecified)
Depositing User: Symplectic Admin
Date Deposited: 28 Apr 2016 12:14
Last Modified: 17 Dec 2022 02:25
DOI: 10.1007/978-3-662-49192-8_29
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3000472