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
2024-01-01
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.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
2023c-CoronaDellaCorte-ETDS.pdf
accesso aperto
Tipologia:
Versione Editoriale
Licenza:
DRM non definito
Dimensione
829.24 kB
Formato
Adobe PDF
|
829.24 kB | Adobe PDF | Visualizza/Apri |
|
Paper_Meas_Eras.pdf
accesso aperto
Tipologia:
Documento in Post-print
Licenza:
DRM non definito
Dimensione
539.54 kB
Formato
Adobe PDF
|
539.54 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
