Abstract
This paper is devoted to the proof of the following theorem: Let 1<c<∞. The number of conjugacy classes of pseudo-Anosov elements f of the group mods with stretching factor λ(f)≤c is finite.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
P. Arnoux and J.-C. Yoccoz, “Construction de diffeomorphismes pseudo-Anosov”, C. R. Acad. Sci.,292, Series 1, No. 1, 75–78 (1981).
L. Bers, “An extremal problem for quasiconformal mappings and a theorem by Thurston”, Acta Math.,141, Nos. 1–2, 73–98 (1978).
S. A. Bleiler, “The Nielsen-Thurston theory of surface automorphisms”, Ann. Math. Studies, No. 111, 397–413 (1987).
S. M. Gersten, “Selected problems”, Ann. Math. Studies, No. 112, 545–551 (1987).
N. V. Ivanov, “Algebraic properties of the Teichmüller modular group”, Dokl. Akad. Nauk SSSR,275, No. 4, 786–789 (1984).
N. V. Ivanov, “Algebraic properties of the mapping class groups of surfaces”, LOMI Preprints, 1985, E-1-95.
N. V. Ivanov, “Subgroups of Teichmüller modular groups and their Frattini subgroups”, Funkts. Analiz Prilozhen.,21, No. 2, 76 (1987).
J. McCarthy, “Normalizers and centralizers of pseudo-Anosov mapping classes”, Preprint, 1982.
J. McCarthy, “A ‘Tits-Alternative’ for subgroups of surface mapping class groups”, Trans. Am. Math. Soc.,291, No. 2, 583–612 (1985).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 167, pp. 111–116, 1988.
Rights and permissions
About this article
Cite this article
Ivanov, N.V. Stretching factors of pseudo-Anosov homeomorphisms. J Math Sci 52, 2819–2822 (1990). https://doi.org/10.1007/BF01099245
Issue Date:
DOI: https://doi.org/10.1007/BF01099245