Iterates of mappings which are almost continuous and open

2010/10/06 by Chris Preston, Preston, Chris
Engineering · Mathematics · #Advanced Control Systems Optimization #Functional Equations Stability Results #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.1010.1156

19 pages

arxiv created 2010/11/20 · arxiv updated 2010/11/23

Abstract

This note presents an approach to studying the iterates of a mapping whose restriction to the complement of a finite set is continuous and open. The main examples to which the approach can be applied are piecewise monotone mappings defined on an interval or a finite graph.

Related

• The closed graph theorem is the open mapping theorem
• Closed graphs and open maps
• On Almost Regular Mappings
• On definable open continuous mappings
• On the Closed Graph Theorem and the Open Mapping Theorem