Coboundary equations of eventually expanding transformations
2003 ◽
Vol 67
(1)
◽
pp. 39-50
Keyword(s):
Let T be an eventually expansive transformation on the unit interval satisfying the Markov condition. The T is an ergodic transformation on (X, ß, μ) where X = [0, 1), ß is the Borel σ-algebra on the unit interval and μ is the T invariant absolutely continuous measure. Let G be a finite subgroup of the circle group or the whole circle group and φ: X → G be a measurable function with finite discontinuity points. We investigate ergodicity of skew product transformations Tφ on X × G by showing the solvability of the coboundary equation φ(x) g (Tx) = λg (x), |λ| = 1. Its relation with the uniform distribution mod M is also shown.
2012 ◽
Vol 82
(3)
◽
pp. 557-564
◽
1982 ◽
Vol 33
(1)
◽
pp. 30-39
◽
1989 ◽
Vol 9
(1)
◽
pp. 101-113
◽
1980 ◽
Vol 32
(6)
◽
pp. 1501-1517
◽
1968 ◽
Vol 19
(2)
◽
pp. 361-361
◽
2001 ◽
Vol 14
(3)
◽
pp. 257-264
◽