Some ergodic properties of the negative slope algorithm
Ishimura, Koshiro ; Nakada, Hitoshi
Osaka J. Math., Tome 44 (2007) no. 1, p. 667-683 / Harvested from Project Euclid
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The notion of the negative slope algorithm was introduced by S. Ferenczi, C. Holton, and L. Zamboni as an induction process of three interval exchange transformations. Then S. Ferenczi and L.F.C. da Rocha gave the explicit form of its absolutely continuous invariant measure and showed that it is ergodic. In this paper we prove that the negative slope algorithm with the absolutely continuous invariant measure is weak Bernoulli. We also show that this measure is derived as a marginal distribution of an invariant measure for a 4-dimensional (natural) extension of the negative slope algorithm. We also calculate its entropy by Rohlin's formula.
Publié le : 2007-09-14
Classification:  11K55,  37A05,  37A25 
@article{1189717427,
     author = {Ishimura, Koshiro and Nakada, Hitoshi},
     title = {Some ergodic properties of the negative slope algorithm},
     journal = {Osaka J. Math.},
     volume = {44},
     number = {1},
     year = {2007},
     pages = { 667-683},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1189717427}
}

Ishimura, Koshiro; Nakada, Hitoshi. Some ergodic properties of the negative slope algorithm. Osaka J. Math., Tome 44 (2007) no. 1, pp.  667-683. http://gdmltest.u-ga.fr/item/1189717427/