Continuous unimodal maps in economic dynamics: On easily verifiable conditions for topological chaos

Liuchun Deng, M. Khan and Tapan Mitra

Journal of Economic Theory, 2022, vol. 201, issue C

Abstract: In this paper, we offer necessary and sufficient conditions for the presence of odd-period cycles and turbulence in a continuous unimodal interval map. The characterizations we present are original both to the economic and the mathematical literature, and go beyond existential assertions to easy verifiability. We apply our two theorems to six different canonical models in the literature on economic dynamics, all being grounded in the fact that their policy functions are given by continuous unimodal maps. An unintended outcome of the work presented here is to alert the economics profession to a richer conception of erratic and chaotic dynamics, one that goes considerably beyond the 1964-1975 Sharkovsky-Li-Yorke emphasis on three-period cycles and on uncountable scrambled sets.

Keywords: Odd-period cycles; Turbulence; Topological chaos; Economic dynamics (search for similar items in EconPapers)
JEL-codes: C60 O11 O40 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:201:y:2022:i:c:s0022053122000369

DOI: 10.1016/j.jet.2022.105446

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