Quaternionic Funnel Structure of the Syracuse Map

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.