Abstract
It is well known that the stability of optimal paths for infinite horizon concave problems is not assured for all discount factors. Along the ideas developed in Boldrin and Montrucchio (IER, 1988), we provide new results of stability which are related to the notion of acyclicity. Some order relations are introduced which can be seen as generalizations of Liapunov theory. Our results are quite complete for one-dimensional case. In higher dimensions we state some new results.
The first author was partially supported by a grant from M.U.R.S.T., National Group on Nonlinear Dynamics in Economics and Social Sciences
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References
J.P. Aubin and A. Cellina, “Differential Inclusions”, Springer-Verlag 1984.
M. Boldrin and L. Montrucchio, “On the Indeterminacy of Capital Accumulation Paths”, Journal of Economic Theory 40 (1986), 26–39.
M. Boldrin and L. Montrucchio, “Acyclicity and Stability for Intertemporal Optimization Models”, International Economic Review 29(1) (1988), 137–146.
M. Boldrin and L. Montrucchio, “Acyclicity and Dynamical Stability: Generalizations and Economic Applications”, MIMEO 1990.
J. Hale, “Asymptotic Behavior of Dissipative Systems”, American Mathematical Society Rhode Island, Providence 1988.
J. P. LaSalle, “The Stability of Dynamical Systems”, Society for Industrial and Applied Mathematics Philadelphia, Pennsylvania 1976.
L. Montrucchio, “Optimal Decisions Over Time and Strange Attractors: an Analysis by the Bellman Principle”, Mathematical Modelling 7 (1986), 341–352.
A. N. Sarkovsky, “Coexistence of Cycles of a Continuous Map of the Line into Itself”, Ukr. Mat. Z. 16 (1964), 61–71.
S. Smale, “Differential Dynamical Systems”, Bulletin of the American Mathematical Society 1967
N. Stokey and R. Lucas and R. Prescott, “Recursive Methods in Economic Dynamics”, Harvard University Press 1989.
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© 1993 Springer-Verlag Berlin Heidelberg
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Montrucchio, L., Persico, N. (1993). Acyclicity of Optimal Paths. In: Gori, F., Geronazzo, L., Galeotti, M. (eds) Nonlinear Dynamics in Economics and Social Sciences. Lecture Notes in Economics and Mathematical Systems, vol 399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58031-4_16
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DOI: https://doi.org/10.1007/978-3-642-58031-4_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56704-2
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