Ergodic baker's transformations
Date
2010-04-21T22:58:16Z
Authors
Bose, C. J.
Grzegorczyk, P.
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Abstract
Let T be a generalized baker's transformation on the unit square with cut function f. We show that if f is monotone non-increasing and bounded away from zero and one then T is ergodic. No topological conditions on f are assumed. Moreover, we prove in this case that T has a weak-Bernoulli generator. Both of these results follow from an exponential rate of contraction in variation by the related Perron-Frobenius operator. The connection between these results and similar facts for interval maps and g-measures is described
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technical reports (mathematics and statistics)