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Titlebook: Algorithms, Fractals, and Dynamics; Y. Takahashi Book 1995 Plenum Press, New York 1995 Homeomorphism.Maxima.Variance.algorithms

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,Koksma’s Inequality and Group Extensions of Kronecker Transformations,We consider methods of establishing ergodicity of group extensions, proving that a class of cylinder flows are ergodic, coalescent and non-squashable. A new Koksma-type inequality is also obtained.
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Quadratic Maps with Maximal Oscillation,Let (..)o≤t≤1 denote the family of quadratic maps .. = 2.(1- ..) - 1 on [-1, 1]. An important aspect of the asymptotics of interates of a map .. is the behaviour of mass distributions along individual orbits.
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The Dynamics of Self-Similar Sets on ,, and Complex Dynamics,We begin with the following theorem (see [3] and [4]).
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,A Short Proof of Even α-Equivalence,α-equivalence of two discrete dynamical systems is defined via continuous actions and vice versa. We present a short proof of the equivalence, bypassing the whole machinery of the restricted orbit equivalence.
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Zweites Kapitel: Das Phänomen „Enhancement“ 80 years ago Borel showed that almost all real numbers are normal to all bases. Some 40 years ago Steinhaus asked whether 2-normality coincides with 3-normality and Cassels answered the question in the negative (see [3]).
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