Zeckendorf Folds, Sturmian Rigidity, and Parry Divergence on the Golden-Mean Shift

Ergodic theory and symbolic dynamics

gen2
ergodic
submitted
The canonical Zeckendorf fold on the Sturmian slice is bijective and realizes the higher-block presentation, giving an exact KL formula and sharp support-constrained Renyi minima in closed form….
Published

April 7, 2026

Ergodic Theory and Dynamical Systems 46 Theorems Ergodic theory and symbolic dynamics

Abstract

The canonical Zeckendorf fold on the Sturmian slice is bijective and realizes the higher-block presentation, giving an exact KL formula and sharp support-constrained Renyi minima in closed form.

Keywords: Sturmian subshifts, Zeckendorf numeration, golden-mean shift, Parry measure, Renyi divergence

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