Recurrence of Integrals of Conditionally Periodic Functionsстатья
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Дата последнего поиска статьи во внешних источниках: 15 февраля 2024 г.
Аннотация:Abstract—A range of issues related to the recurrence of integrals of conditionally periodic functions with zero mean value is discussed. In the case of smooth functions on the torus, the recurrence of integrals obviously holds for all initial phases. A new observation is that, for almost all initial phases, the recurrence property simultaneously holds not only for integrals, but also for phase points on the torus. Moreover, this result is also valid in the case where the corresponding functions on the torus are only continuous. These observations are extended to the general case of ergodic transformations of compact metric spaces with Carathéodory measure.Keywords: conditionally periodic function, frequencies, recurrence, Carathéodory measure, Hopf’s theorem