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Title: | Topological formulation of termination properties of iterates of functions | Authors: | KUIJPERS, Bart GEERTS, Floris |
Issue Date: | 2004 | Publisher: | Elsevier | Source: | Information Processing Letters, 89(1). p. 31-35 | 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 f :Rn →Rn as input and ask, for example, whether this function is mortal, nilpotent, terminating, or reaches a fixed point on a given point in Rn.We associate topologies to functions f :Rn→Rn 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 Rn is undecidable for n>1. | Document URI: | http://hdl.handle.net/1942/657 | ISSN: | 0020-0190 | e-ISSN: | 1872-6119 | DOI: | 10.1016/j.ipl.2003.09.012 | ISI #: | 000187800500006 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2005 |
Appears in Collections: | Research publications |
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