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arXiv · 1801.09806

A proof of Jones' conjecture

Jonathan Jaquette
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Abstract

In this paper, we prove that Wright's equation $y'(t) = - αy(t-1) \{1 + y(t)\}$ has a unique slowly oscillating periodic solution for parameter values $α\in (\tfracπ{2}, 1.9]$, up to time translation. This result proves Jones' Conjecture formulated in 1962, that there is a unique slowly oscillating periodic orbit for all $ α> \tfracπ{2}$. Furthermore, there are no isolas of periodic solutions to Wright's equation; all periodic orbits arise from Hopf bifurcations.

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Jonathan Jaquette. 2018-01-30. A proof of Jones' conjecture. https://arxiv.org/abs/1801.09806

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