Uniform Measures On Inverse Limit Spaces
Motivated by problems from dynamic economic models, we consider the problem of defining a uniform measure on inverse limit spaces. Let f be a function from a compact metric space X into itself where f is continuous, onto and piecewise one-to-one. Let Y be the inverse limit of (X,f). Then starting with a measure m1 on the Borel sets of X, we recursively construct a sequence of probability measures (m1,m2,...) on the Borel sets of X satisfying mn(A)=mn+1[B] for each Borel set A and n=1,2,... and B is the preimage of A under f. This sequence of probability measures is then uniquely extended to a probability measure on the inverse limit space Y. If m1 is a uniform measure, we argue that the measure induced on the inverse limit space by the recursively constructed sequence of measures is a uniform measure. As such, the measure has uses in economic theory for policy evaluation and in dynamical systems in providing an ambient measure (when Lebesgue measure is not available) with which to define an SRB measure or a metric attractor for the shift map on the inverse limit space.
|Date of creation:||2008|
|Date of revision:|
|Publication status:||Forthcoming in Applicable Analysis|
|Contact details of provider:|| Postal: Purnell Hall, Newark, Delaware 19716|
Phone: (302) 831-2565
Fax: (302) 831-6968
Web page: http://lerner.udel.edu/departments/economics/department-economics/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Robert E. Lucas, Jr. & Nancy L. Stokey, 1985.
"Money and Interest in a Cash-in-Advance Economy,"
NBER Working Papers
1618, National Bureau of Economic Research, Inc.
- Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
- Grandmont Jean-michel, 1983.
"On endogenous competitive business cycles,"
CEPREMAP Working Papers (Couverture Orange)
- Kennedy, Judy & Stockman, David R. & Yorke, James A., 2008. "The inverse limits approach to chaos," Journal of Mathematical Economics, Elsevier, vol. 44(5-6), pages 423-444, April.
- Michener, Ronald & Ravikumar, B., 1998. "Chaotic dynamics in a cash-in-advance economy," Journal of Economic Dynamics and Control, Elsevier, vol. 22(7), pages 1117-1137, May.
- Medio, Alfredo & Raines, Brian, 2007. "Backward dynamics in economics. The inverse limit approach," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1633-1671, May.
- Kennedy, Judy A. & Stockman, David R., 2008. "Chaotic equilibria in models with backward dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 939-955, March.
When requesting a correction, please mention this item's handle: RePEc:dlw:wpaper:08-25.. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Saul Hoffman)
If references are entirely missing, you can add them using this form.