Geodesic
A two parameter family of piecewise linear transformations with negative slope
Acta mathematica Universitatis Comenianae, Tome 81 (2012) no. 1, pp. 15-30 
F. Hofbauer; F. Hofbauer. A two parameter family of piecewise linear transformations with negative slope. Acta mathematica Universitatis Comenianae, Tome 81 (2012) no. 1, pp. 15-30. http://geodesic.mathdoc.fr/item/AMUC_2012_81_1_a2/
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     author = {F. Hofbauer and F. Hofbauer},
     title = { A two parameter family of piecewise linear transformations with negative slope},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {15--30},
     year = {2012},
     volume = {81},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2012_81_1_a2/}
}
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Voir la notice de l'article provenant de la source Comenius University

We study a two parameter family of piecewise linear transformations on the interval [0, 1] which have negative slope. We show that the nonwandering set consists of finitely many periodic orbits and an invariant set L which is topologically transitive and the disjoint union of finitely many closed intervals. We determine the number of these intervals.