Most automorphisms of a hyperbolic group have very simple dynamics
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 4, pp. 507-517. 
@article{ASENS_2000_4_33_4_507_0,
     author = {Levitt, Gilbert and Lustig, Martin},
     title = {Most automorphisms of a hyperbolic group have very simple dynamics},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {507--517},
     publisher = {Elsevier},
     volume = {Ser. 4, 33},
     number = {4},
     year = {2000},
     doi = {10.1016/s0012-9593(00)00120-8},
     mrnumber = {2002d:20066},
     zbl = {0997.20043},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(00)00120-8/}
}
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Levitt, Gilbert; Lustig, Martin. Most automorphisms of a hyperbolic group have very simple dynamics. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 4, pp. 507-517. doi : 10.1016/s0012-9593(00)00120-8. http://www.numdam.org/articles/10.1016/s0012-9593(00)00120-8/

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