Octagonal continued fraction and diagonal changes
Mauro Artigiani
TL;DR
This paper demonstrates that the octagon Farey map is an accelerated version of the diagonal changes algorithm, providing insights into their relationship within the context of continued fractions.
Contribution
It establishes a connection between the octagon Farey map and the diagonal changes algorithm, showing one as an acceleration of the other.
Findings
The octagon Farey map is an acceleration of the diagonal changes algorithm.
This relationship clarifies the dynamics of continued fractions in octagonal settings.
The result simplifies understanding of the octagon Farey map's behavior.
Abstract
In this short note we show that the octagon Farey map introduced by Smillie and Ulcigrai is an acceleration of the diagonal changes algorithm introduced by Delecroix and Ulcigrai.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Meromorphic and Entire Functions