Quaternionic Funnel Structure of the Syracuse Map

Ricardo Hernández Reveles

doi:10.5281/zenodo.19775729

April 26, 2026Open Access

Quaternionic Funnel Structure of the Syracuse Map

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Key Points

This research investigates the quaternionic encoding and its implications for the Syracuse map and Markov chains.
Utilized quaternionic encoding Q²=−3 to analyze the Syracuse map.
Applied 3-state Markov chain techniques focusing on ergodic drift and Cramér large deviations.
Explored affine group structures and SU(2) density in the context of the dynamical system.
Identified the ergodic drift D=log(3/4)<0, indicating stability in the system.
Demonstrated connections between Markov chains and quaternionic structures with implications for dynamics.
Characterized the model contraction criterion relevant to the behavior of the Syracuse map.

Implication

Examines quaternionic structures in the Syracuse map, suggesting new insights into dynamical systems.

Abstract

Quaternionic encoding Q²=−3 of the Syracuse map, 3-state Markov chain (rank-1 kernel, exact gap 1), affine group Γ_p ≤ AGL(1,p), gateway set G_p°, Legendre channel, ergodic drift D=log(3/4)<0, CLT, Cramér large deviations, SU(2) density, and model contraction criterion.

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Cite This Study

Ricardo Hernández Reveles (2026) studied this question.

synapsesocial.com/papers/69f04e5b727298f751e724e1 https://doi.org/10.5281/zenodo.19775729

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Quaternionic Funnel Structure of the Syracuse Map

Key Points

Implication

Abstract

Discussion

Cite This Study

Quaternionic Funnel Structure of the Syracuse Map

Key Points

Implication

Abstract

Discussion

Cite This Study

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