Time, space and equilibrium means of continuous vector functions on the phase space of a dynamical system

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.
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