Constant slope models for finitely generated maps

Samuel Roth

doi:10.3934/dcds.2018106

Article Contents

2018, Volume 38, Issue 5: 2541-2554. Doi: 10.3934/dcds.2018106

This issue Previous Article Stability of the distribution function for piecewise monotonic maps on the interval Next Article Global existence in the critical space for the Thirring and Gross-Neveu models coupled with the electromagnetic field

Constant slope models for finitely generated maps

Samuel Roth

Silesian University in Opava, Na Rybničku 626/1, 746 01 Opava, Czech Republic

Received: June 30, 2017

Published: June 2018

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Abstract

We study countably monotone and Markov interval maps. We establish sufficient conditions for uniqueness of a conjugate map of constant slope. We explain how global window perturbation can be used to generate a large class of maps satisfying these conditions.

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Mathematics Subject Classification: Primary: 37E05; Secondary: 37B40.

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Figure 1. The production of a finitely generated map

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Table 1. Some countably monotone maps from the literature -cf. Section 7.2

Graph
Source	[3,§ 7.1]	[4,§ 4]	[9,§ 8]	[3,§ 7.2.1]	[3,§ 7.2.1]
Vere-Jones classification	Recurrent	Transient	Recurrent	Recurrent	Transient
Finitely generated	No	No	No	Yes	Yes
Constant slope models	None	For all $\lambda\geq\exp h(f)$	For all $\lambda\geq\exp h(f)$	Unique, $\lambda=\exp h(f)$	None

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References

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