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Volume 37 (2024)

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Far East Journal of Dynamical Systems

Rⁿ, n³ 2 to itself, due to Kannan, Saradhi and Seshasai. For this purpose, we consider instead pairs of maps from Rⁿ, n ³ 1 to itself, and we show that the set of “all possible contact orders” for two arbitrary continuous maps f, g : Rⁿ ® Rⁿ may appear as any subset of the naturals.

Far East Journal of Dynamical Systems
Volume 7, Issue 1, Pages 65 - 75 (June 2005)

A ŠARKOVSKII-TYPE THEOREM FOR PAIRS OF MAPS
Marcelo Polezzi (Brazil) and Claudemir Aniz (Brazil)

Abstract:
In this paper, we generalize an analogue of Šarkovskii’s Theorem for maps from Rⁿ, n ³ 2 to itself, due to Kannan, Saradhi and Seshasai. For this purpose, we consider instead pairs of maps from Rⁿ, n ³ 1 to itself, and we show that the set of “all possible contact orders” for two arbitrary continuous maps f, g : Rⁿ ® Rⁿ may appear as any subset of the naturals.

Keywords and phrases: discrete dynamical systems, Šarkovskii’s theorem.

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