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Dehn twists and pseudo-Anosov diffeomorphisms. (English) Zbl 0618.58027
The author shows that it is possible to obtain many pseudo-Anosov diffeomorphisms from Dehn twists. Let M be a closed and oriented surface. The set of isotopy classes of simply connected closed curves on M is denoted by \({\mathcal S}(M)\), the set of isotopy classes of diffeomorphisms by \(\pi_ 0(Diff(M))\). He proves the following theorem: Let f be in \(\pi_ 0(Diff(M))\) and let \(\gamma\) be in \({\mathcal S}(M)\). If the orbit of \(\gamma\) under f fills M, then \(T^ n_{\gamma} f\) is a pseudo-Anosov class except for at most 7 consecutive values of n.
Reviewer: A.Reinfelds (Riga)

37D99 Dynamical systems with hyperbolic behavior
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[1] [FLP] Fathi, A., Laudenbach, F., Poenaru, V.: Travaux de Thurston sur les surfaces. Astérisque66-67 (1979)
[2] [LM] Long, D., Morton, H.: Hyperbolic 3-manifolds and surface automorphisms. Preprint
[3] [Ma] Masur, H.: Two boundaries of Teichmüller space. Duke Math. J.49, 183-190 (1982) · Zbl 0508.30039 · doi:10.1215/S0012-7094-82-04912-2
[4] [Pa1] Papadopoulos, A.: Difféomorphismes pseudo-Anosov et automorphismes symplectiques de l’homologie. Ann. Scient. Éc. Norm Super., IV. Ser.15, 543-546 (1982) · Zbl 0539.58023
[5] [Pa2] Papadopoulos, A.: Deux remarques sur la géométrie symplectique de l’espace des feuilletages mesurés sur une surface. Ann. Inst. Fourier (in press) (1986)
[6] [Pa3] Papadopoulos, A.: Geometric intersection functions and Hamiltonian flows on the space of measured foliations on a surface. Preprint Institute of Advanced Studies · Zbl 0608.58036
[7] [Re] Rees, M.: An alternative approach to the ergodic theory of measured foliations on surfaces. Ergodic Theory Dyn. Syst.1, 461-488 (1981) · Zbl 0539.58018
[8] [St] Strebel, K.: Quadratic differentials. Berlin, Heidelberg, New York, Tokyo: Springer 1984 · Zbl 0547.30001
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