Geodesic
Time, space and equilibrium means of continuous vector functions on the phase space of a~dynamical system
Sbornik. Mathematics, Tome 201 (2010) no. 3, pp. 339-354

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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. Bibliography: 18 titles.
Keywords: dynamical system, space mean, equilibrium mean, time mean, pressure. 
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     author = {B. M. Gurevich and A. A. Tempel'man},
     title = {Time, space and equilibrium means of continuous vector functions on the phase space of a~dynamical system},
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B. M. Gurevich; A. A. Tempel'man. Time, space and equilibrium means of continuous vector functions on the phase space of a~dynamical system. Sbornik. Mathematics, Tome 201 (2010) no. 3, pp. 339-354. http://geodesic.mathdoc.fr/item/SM_2010_201_3_a1/