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Abstract

In discrete calendar time, let us consider once more a competitive economy under stationary fundamentals, containing n goods, and let its deterministic temporary equilibrium,1 when all economic agents choose their best programs with reference to two periods only, “present” and “future”, be expressed, period after period, by

$$e[p(t),p(t + 1);\theta ] = 0(t = 1,2,...),$$
(30.1)

where \(\theta \in {\Re ^m}\) is a vector of parameters expressing, for instance, the mech- anism used by agents to forecast future prices.

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Reference

  1. See § 26.2.

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  2. In continuous time, the differential equation equivalent to (30.2) was introduced in 1838 by the Belgian mathematician Verhulst to study the dynamics of human populations.

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  3. For instance, Devaney (1989, pp.268–272).

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  4. The book by Nusse and Yorke (1994) presents many numerical explorations on the trajectories generated by the logistic map, and by other one- or two-dimensional maps; for a picture of a path generated by the logistics, see, for instance, their figure at p.47.

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  5. One of the first monographs on dynamic systems in discrete time is Collet and Eckmann (1980).

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  6. Maybe the auctioneer.

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  7. Here we are interested only in this type of analysis.

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  8. See also Devaney (1989, p.269).

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  9. It is well-known that in the most mathematically oriented sciences the greatest part of the phenomena under study are governed by non-linear equations.

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  10. See Kloeden (1979, p.174); the definition of Sharkovsky’s order can be seen in Drazin (1992, pp.132–133).

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  11. See also Kaplan and Yorke (1979).

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  12. But remember the point of view expressed by Ruelle (1988), reported at the end of § 30.1.

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  13. See § 26.3.

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© 2000 Springer-Verlag Berlin Heidelberg

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Nicola, P. (2000). Deterministic Chaos. In: Mainstream Mathematical Economics in the 20th Century. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04238-0_30

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  • DOI: https://doi.org/10.1007/978-3-662-04238-0_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08638-0

  • Online ISBN: 978-3-662-04238-0

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