We study the measurable dynamical properties of the interval map generated by the model-case erasing substitution rho, defined by rho (00) = empty word, rho (01) = 1, rho (10) = 0, rho (11) = 01. We prove that, although the map is singular, its square preserves the Lebesgue measure and is strongly mixing, thus ergodic, with respect to it. We discuss the extension of the results to more general erasing maps.

Mixing properties of erasing interval maps

Corona, D
;
Della Corte, A
2023-01-01

Abstract

We study the measurable dynamical properties of the interval map generated by the model-case erasing substitution rho, defined by rho (00) = empty word, rho (01) = 1, rho (10) = 0, rho (11) = 01. We prove that, although the map is singular, its square preserves the Lebesgue measure and is strongly mixing, thus ergodic, with respect to it. We discuss the extension of the results to more general erasing maps.
2023
262
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11581/470754
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