On the minimum ergodic average and minimal systems

• Autores: Manuel Saavedra, Helmuth Villavicencio
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 24, Nº. 3, 2022, págs. 457-466
• Idioma: inglés
• DOI: 10.56754/0719-0646.2403.0457
• Enlaces
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• Resumen
  • español

    Resumen Demostramos algunas equivalencias asociadas con el caso cuando el tiempo inferior promedio es mínimo. Además, caracterizamos los sistemas minimales a través de la positividad de medidas invariantes en conjuntos abiertos y también los promedios ergódicos mínimos. Finalmente, mostramos que un sistema minimal admite un conjunto abierto cuya medida es mínima con respecto a un conjunto de medidas ergódicas y su valor puede ser elegido en [0, 1].

  • English

    Abstract We prove some equivalences associated with the case when the average lower time is minimal. In addition, we characterize the minimal systems by means of the positivity of invariant measures on open sets and also the minimum ergodic averages. Finally, we show that a minimal system admits an open set whose measure is minimal with respect to a set of ergodic measures and its value can be chosen in [0, 1].

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