## The Perron-Frobenius operator on BV. I.(English)Zbl 1084.11506

Summary: In this paper, we determine the upper bound $$\gamma_n$$ of $$\text{var}\,U^n f/\text{var}\,f$$, when $$f$$ varies in the collection of non-constant monotone functions on $$I=[0,1]$$.

### MSC:

 11K50 Metric theory of continued fractions 37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)

### Keywords:

functions of bounded variation; continued fractions
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