Abstract
Basic sets1 of the pseudo-Anosov (A—) diffeomorphisms and homeomorphisms generate an interesting class of non-orientable foliations. R. V. Plykin, and later on V. Z. Grines and A. Yu. Zhirov used such foliations to obtain a classification of A—diffeomorphisms on closed surfaces. As an introductory reading we recommend the classical survey of
S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817.
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Bibliographic Notes
Anosov, D. V. 1967 Geodesic flows on closed Riemannian manifolds with negative curvature, Trudy Mat. Inst. Steklov 90, Translation: Proc. Steklov Inst. Math. 90.
Fathi, A., Laudenbach, F., and Poénaru, Z., 1979 Travaux de Thurston sur les surfaces, Séminaire Orsay, France, Astérisque 66–67.
Plykin, R. V., 1974 Sourses and sinks of A-diffeomorphisms on surfaces, Mat. Sbornik 94, 243–264, Translation: Mat. Sbornik.
Plykin, R. V., 1984 On the geometry of hyperbolic attractors of smooth cascades, Russian Math. Surveys 39, no. 6, 85–131.
Thurston W. P., 1988 On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer Math. Soc. 19, 417–431.
Zhirov, A. Yu., 1995 Hyperbolic attractors of diffeomorphisms of orientable surfaces. I, Russian Acad. Sci. Sb. Math. 82, 135–174.
Zhirov, A. Yu., 1995 Hyperbolic attractors of diffeomorphisms of orientable surfaces. II, Russian Acad. Sci. Sb. Math. 83, 23–65.
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© 2001 Springer-Verlag Berlin Heidelberg
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Nikolaev, I. (2001). Diffeomorphisms of Surfaces. In: Foliations on Surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04524-4_10
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DOI: https://doi.org/10.1007/978-3-662-04524-4_10
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