A bound for the rate of decrease of correlation in one-dimensional dynamical systems
Let T be a mapping of [0,1] into itself such that there exists a finite partition \(0=a_ 0<a_ 1<...<a_ k=1\) for which T is monotone and of class \(C^ 1\) on each \((a_{i-1},a_ i)\), the function 1/\(| T'|\) is of bounded variation on each \([a_{i-1},a_ i]\) and \(\inf_{x}| T'(x)| >1.\) Then T is known to have an invariant measure \(\mu\) absolutely continuous with respect to Lebesgue measure. For \(f,g\in C^ 1[0,1]\) the n-th correlation is defined by \[ K_ n(f,g)=\int f(T^ nx)g(x)d\mu -\int f(x)d\mu\int g(x)d\mu. \] The author investigates the rate of decrease of \(K_ n(f,g)\) for mixings T.
scientific article; zbMATH DE number 3875613