The Inverse Limits Approach to Chaos Judy Kennedy A,B, David R
Available online at www.sciencedirect.com Journal of Mathematical Economics 44 (2008) 423–444 The inverse limits approach to chaos Judy Kennedy a,b, David R. Stockman c,∗, James A. Yorke d a Departmentof Mathematical Sciences, University of Delaware, Newark, DE 19716, United States b Department of Mathematics, Lamar University, Beaumont, TX 77710, United States c Department of Economics, University of Delaware, Newark, DE 19716, United States d Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, United States Received 27 March 2006; received in revised form 31 October 2007; accepted 3 November 2007 Available online 22 November 2007 Abstract When analyzing a dynamic economic model, one fundamental question is are the dynamics simple or chaotic? Inverse limits,as an area of topology, has its origins in the 1920s and since the 1950s has been very useful as a means of constructing “pathological” continua. However, since the 1980s, there is a growing literature linking dynamical systems with inverse limits. In this paper, we review some results from this literature and apply them to the cash-in-advance model of money. In particular, we analyze the inverse limit of the cash-in-advance model of money and illustrate how information about the inverse limit is useful for detecting or ruling out complicated dynamics. © 2007 Elsevier B.V. All rights reserved. JEL Classification: C6; E3; E4 Keywords: Chaos; Inverse limits; Continuum theory; Topological entropy; Cash-in-advance 1. Introduction An equilibrium of a dynamic economic model can often be characterized as a solution to a dynamical system. One fundamental question when analyzing such a model is are the dynamics simple or chaotic? There are numerous definitions and measurements for chaos.
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