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Density theorems for closed orbits. (English) Zbl 0668.58043
Proc. 21st. Int. Taniguchi Symp., Katata/Japan, Conf., Kyoto/Japan 1987, Lect. Notes Math. 1339, 182-202 (1988).
[For the entire collection see Zbl 0638.00022.]
From the introduction: This is a survey article concerning one of the applications of number theoretic ideas to geometry. I will show several geometric analogues of density theorems in number theory. Two years ago, T. Sunada [Curvature and topology of Riemannian manifolds, Lect. Notes Math. 1201, 266-284 (1986; Zbl 0605.58046)], wrote the same kind of article. This note is in some part a continuation of it. But I emphasize the application of \({\mathcal L}\)-function, that is “How to influence the pole of \({\mathcal L}\)-function to the density of prime closed orbits.”
Reviewer: B.A.Shcherbakov

37G99 Local and nonlocal bifurcation theory for dynamical systems