Veech, William A. Quasiminimal invariants for foliations of orientable closed surfaces. (English) Zbl 0697.57012 Proc. Indian Acad. Sci., Math. Sci. 99, No. 1, 27-48 (1989). The author extends the Katok’s boundedness result to some quasiminimal orientable foliations of closed oriented surfaces with a more general singular set. This allows to interpret Katok’s bound in terms of the interval exchange transformations. Reviewer: D.Motreanu Cited in 4 Documents MSC: 57R30 Foliations in differential topology; geometric theory 37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) Keywords:cone of invariant measures; quasiminimal orientable foliations of closed oriented surfaces; Katok’s bound; interval exchange transformations × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Aranson, S. H., The absence of nonclosed Poisson-stable semi-trajectories and trajectories doubly asymptotic for a double limit cycle for dynamical systems of the first degree of structural instability on orientable two-dimensional manifolds, Math. Sb., 76, 214-230 (1968) · Zbl 0159.11901 [2] Bebutoff, M.; Stepanoff, W., Sur la mesure invariente dans les systèmes dynamiques qui ne different que par le temps, Recueil Math. (Mat. Sbornik), 7, 143-166 (1940) · JFM 66.0434.02 [3] Cherry, T. M., Analytic quasi-periodic curves of discontinuous type on a torus, Proc. London Math. Soc., 44, 175-215 (1937) · Zbl 0019.11503 · doi:10.1112/plms/s2-44.3.175 [4] Hartman, P., Ordinary different equations, 1973-1973 (1964), New York: Wiley and Sons, New York · Zbl 0125.32102 [5] Katok, A. B., Invariant measures of flows on oriented surfaces, Sov. Math. Dokl., 14, 1104-1108 (1973) · Zbl 0298.28013 [6] Keane, A., Interval exchange transformations, Math. Z., 141, 77-102 (1975) · Zbl 0278.28010 · doi:10.1007/BF01236981 [7] Maier, A. G., Trajectories on the closed orientable surfaces, Math. Sb., 12, 71-84 (1943) · Zbl 0063.03856 [8] Rauzy, G., Echanges d’Intervalles et Transformations Induites, Acta Arith., 34, 315-328 (1978) · Zbl 0414.28018 [9] Veech, W. A., Interval exchange transformations, J. d’Anal. Math., 33, 222-278 (1978) · Zbl 0455.28006 · doi:10.1007/BF02790174 [10] Weyl, H., The concept of a Riemann surface (1964), Reading: Addison-Wesley Publ. Co., Reading This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.