Fixed points imply chaos for a class of differential inclusions that arise in economic models
Authors:
Brian E. Raines and David R. Stockman
Journal:
Trans. Amer. Math. Soc. 364 (2012), 2479-2492
MSC (2010):
Primary 34A60, 54H20, 37B20, 37D45
DOI:
https://doi.org/10.1090/S0002-9947-2012-05377-3
Published electronically:
January 19, 2012
MathSciNet review:
2888216
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We consider multi-valued dynamical systems with continuous time of the form , where
is a set-valued function. Such models have been studied recently in mathematical economics. We provide a definition for chaos,
-chaos and topological entropy for these differential inclusions that is in terms of the natural
-action on the space of all solutions of the model. By considering this more complicated topological space and its
-action we show that chaos is the `typical' behavior in these models by showing that near any hyperbolic fixed point there is a region where the system is chaotic,
-chaotic, and has infinite topological entropy.
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Additional Information
Brian E. Raines
Affiliation:
Department of Mathematics, Baylor University, Waco, Texas 76798
Email:
brian_raines@baylor.edu.
David R. Stockman
Affiliation:
Department of Economics, University of Delaware, Newark, Delaware 19716
Email:
stockman@udel.edu.
DOI:
https://doi.org/10.1090/S0002-9947-2012-05377-3
Keywords:
Chaos,
fixed point,
multi-valued dynamical systems
Received by editor(s):
August 13, 2009
Received by editor(s) in revised form:
April 16, 2010
Published electronically:
January 19, 2012
Additional Notes:
The first author was supported by NSF grant 0604958
The second author would like to thank the Lerner College of Business & Economics for its generous summer research support.
Article copyright:
© Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.