Time, space and equilibrium averages for continuous vector functions on the phase space of a dynamical systemстатья
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Дата последнего поиска статьи во внешних источниках: 6 апреля 2016 г.
Аннотация:For a dynamical system $ \tau$ with 'time' $ \mathbb Z^d$ and compact phase space $ X$, we introduce three subsets of the space $ \mathbb R^m$ related to a continuous function $ f\colon X\to\mathbb R^m$: the set of time means of $ f$ and two sets of space means of $ f$, namely those corresponding to all $ \tau$-invariant probability measures and those corresponding to some equilibrium measures on $ X$. The main results concern topological properties of these sets of means and their mutual position.