Inverse limit spaces arising from problems in economics

Topology and its Applications

Volumn 153, Issue 18, 2006, Pages 3437-3449

  Medio, Alfredo ^a   Raines, Brian E ^b  

^a UNIVERSITY OF UDINE   (Italy)

^b BAYLOR UNIVERSITY   (United States)

Author keywords

Attractor; Continuum; Economics; Indecomposable; Invariant set; Inverse limits; Unimodal

Indexed keywords

EID: 33750031532     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2006.03.006     Document Type: Article

References (22)

1. Azariadis C. Intertemporal Macroeconomics (1993), Blackwell, Cambridge, MA
2. Barge M., Brucks K., and Diamond B. Self-similarity in inverse limit spaces of the tent family. Proc. Amer. Math. Soc. 124 11 (1996) 3563-3570
3. Barge M., and Diamond B. Homeomorphisms of inverse limit spaces of one-dimensional maps. Fund. Math. 146 2 (1995) 171-187
4. Barge M., and Ingram W.T. Inverse limits on [0, 1] using logistic bonding maps. Topology Appl. 72 2 (1996) 159-172
5. Benhabib J., and Day R. A characterization of erratic dynamics in the overlapping generations model. Journal of Economic Dynamics and Control 4 (1982) 37-55
6. Bowen R. A horseshoe with positive measure. Invent. Math. 29 3 (1975) 203-204
7. Brucks K., and Bruin H. Subcontinua of inverse limit spaces of unimodal maps. Fund. Math. 160 3 (1999) 219-246
8. Bruin H. Inverse limit spaces of post-critically finite tent maps. Fund. Math. 165 2 (2000) 125-138
9. Bruin H., Keller G., Nowicki T., and van Strien S. Wild Cantor attractors exist. Ann. of Math. (2) 143 1 (1996) 97-130
10. Gale D. Pure exchange equilibrium of dynamic economic models. Journal of Economic Theory 6 (1973) 12-36
11. Ingram W.T. Inverse Limits (2000), Sociedad Matemática Mexicana, México
12. Ingram W.T. Inverse limits on [0, 1] using piecewise linear unimodal bonding maps. Proc. Amer. Math. Soc. 128 1 (2000) 279-286
13. Ingram W.T., and Mahavier W.S. Interesting dynamics and inverse limits in a family of one-dimensional maps. Amer. Math. Monthly 111 3 (2004) 198-215
14. Jonker L., and Rand D. Bifurcations in one dimension. I. The nonwandering set. Invent. Math. 62 3 (1981) 347-365
15. Kailhofer L. A partial classification of inverse limit spaces of tent maps with periodic critical points. Topology Appl. 123 2 (2002) 235-265
16. Kelley J.L. General Topology (1975), Springer, New York Reprint of the 1955 edition (Van Nostrand, Toronto, Ont.), Graduate Texts in Mathematics, No. 27
17. J. Kennedy, D. Stockman, J. Yorke, Inverse limits and an implicitly defined difference equation from economics, Preprint, pp. 1-34
18. Medio A. Chaotic Dynamics: Theory and Applications to Economics (1992), Cambridge University Press, Cambridge
19. Milnor J. On the concept of attractor. Comm. Math. Phys. 99 2 (1985) 177-195
20. Raines B.E. Inverse limits on [0, 1] using sequences of piecewise linear unimodal bonding maps. Topology Appl. 124 (2002) 159-170
21. B.E. Raines, One-dimensional dynamics and inverse limits, D.Phil. thesis, Oxford University, 2002
22. Raines B.E. Inhomogeneities in non-hyperbolic one-dimensional invariant sets. Fund. Math. 182 3 (2004) 241-268