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arXiv · 2512.20147

Triod twist cycles and circle rotations

Sourav Bhattacharya·Ashish Yadav
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Abstract

We study the problem of relating cycles on a \emph{triod} $Y$ to \emph{circle rotations}. We prove that the simplest cycles on a \emph{triod}~$Y$ with a given \emph{rotation number}~$\rho$, called \emph{triod--twist cycles} are conjugate, via a piece-wise monotone map of \emph{modality} at most~$m + 3$, where~$m$ is the \emph{modality} of~$P$ to the rotation on~$S^1$ by angle~$\rho$, restricted to one of its cycles.

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Sourav Bhattacharya, Ashish Yadav. 2025-12-23. Triod twist cycles and circle rotations. https://arxiv.org/abs/2512.20147

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