Topological formulation of termination properties of iterates of functions |
| |
Authors: | Floris Geerts |
| |
Affiliation: | a University of Helsinki, HIIT Basic Research Unit, PO Box 26, 00014 Helsinki, Finland b University of Limburg (LUC), Department of Mathematics, Physics and Computer Science, 3590 Diepenbeek, Belgium |
| |
Abstract: | We consider a number of decision problems, that appear in the dynamical systems and database literature, concerning the termination of iterates of real functions. These decision problems take a function as input and ask, for example, whether this function is mortal, nilpotent, terminating, or reaches a fixed point on a given point in . We associate topologies to functions and study some basic properties of these topologies. The contribution of this paper is a translation of the above mentioned decision problems into decision problems concerning well-known properties of topologies, e.g., connectivity. We also show that connectivity of topologies on is undecidable for n>1. |
| |
Keywords: | Decision problems Iterates of functions Dynamical systems Fixed points Transitive closure Topology Databases |
本文献已被 ScienceDirect 等数据库收录! |
|