Geodesic
Recurrent Transformation Groups
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 564-575

Voir la notice de l'article provenant de la source Cambridge University Press

Let (X, T, π) denote a flow, where X is a compact topological space metrizable by d, and T is a closed non-trivial subgroup of the reals under addition. T is recurrent if and only if for each and s > 0, there exists t > s such that x ∈ X implies . If T is almost-periodic, then T is both recurrent and distal. In §§ 4 and 5, it is shown that, under more stringent hypotheses, the recurrence of T is neither a necessary nor a sufficient condition for T to be distal. Let S be a closed non-trivial subgroup of T. It is shown in § 3 that T is recurrent if and only if S is recurrent. From this result, we obtain a solution to a problem posed by Nemyckiĭ (16, p. 492, Problem 6). 
Christiansen, R. A. Recurrent Transformation Groups. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 564-575. doi: 10.4153/CJM-1969-064-1
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