Bers and Hénon, Painlevé and Schrödinger
Cantat, Serge
Duke Math. J., Tome 146 (2009) no. 1, p. 411-460 / Harvested from Project Euclid
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In this article, we pursue the study of the holomorphic dynamics of mapping class groups on two-dimensional character varieties, also called trace-map dynamics in the literature, as initiated in [44] (see also [20]). We show that the dynamics of pseudo-Anosov mapping classes resembles in many ways the dynamics of Hénon mappings, and then we apply this idea to answer open questions concerning ¶ (1) the geometry of discrete and faithful representations of free groups into ${\rm SL}(2,\mathbf{C}),$ ¶ (2) the dynamics of Painlevé sixth equations, and ¶ (3) the spectrum of certain discrete Schrödinger operators
Publié le : 2009-09-15
Classification:  37F,  47B,  37A,  37C,  37F,  34M,  57M,  30F40,  47B39 
@article{1251120009,
     author = {Cantat, Serge},
     title = {Bers and H\'enon, Painlev\'e and Schr\"odinger},
     journal = {Duke Math. J.},
     volume = {146},
     number = {1},
     year = {2009},
     pages = { 411-460},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1251120009}
}

Cantat, Serge. Bers and Hénon, Painlevé and Schrödinger. Duke Math. J., Tome 146 (2009) no. 1, pp.  411-460. http://gdmltest.u-ga.fr/item/1251120009/