Weak mixing properties of interval exchange transformations and translation flows

2018 ◽  
Vol 146 (2) ◽  
pp. 391-426
Author(s):  
Artur Avila ◽  
Martin Leguil
Keyword(s):  
Interval Exchange ◽  
Weak Mixing ◽  
Mixing Properties ◽  
Interval Exchange Transformations

scholarly journals Weak mixing for interval exchange transformations and translation flows

2007 ◽  
Vol 165 (2) ◽  
pp. 637-664 ◽  
Author(s):  
Artur Ávila Cordeiro de Melo ◽  
Giovanni Forni
Keyword(s):  
Interval Exchange ◽  
Weak Mixing ◽  
Interval Exchange Transformations

scholarly journals On the mixing properties of piecewise expanding maps under composition with permutations, II: Maps of non-constant orientation

2016 ◽  
Vol 16 (03) ◽  
pp. 1660013 ◽  
Author(s):  
Nigel P. Byott ◽  
Congping Lin ◽  
Yiwei Zhang
Keyword(s):  
Piecewise Linear ◽  
Unit Interval ◽  
Interval Exchange ◽  
Expanding Maps ◽  
Mixing Properties ◽  
Linear Maps ◽  
Piecewise Linear Maps ◽  
Fold Map ◽  
Constant Slope ◽  
Piecewise Expanding Maps

For an integer [Formula: see text], let [Formula: see text] be the partition of the unit interval [Formula: see text] into [Formula: see text] equal subintervals, and let [Formula: see text] be the class of piecewise linear maps on [Formula: see text] with constant slope [Formula: see text] on each element of [Formula: see text]. We investigate the effect on mixing properties when [Formula: see text] is composed with the interval exchange map given by a permutation [Formula: see text] interchanging the [Formula: see text] subintervals of [Formula: see text]. This extends the work in a previous paper [N. P. Byott, M. Holland and Y. Zhang, DCDS 33 (2013) 3365–3390], where we considered only the “stretch-and-fold” map [Formula: see text].

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