## Algorithms, fractals, and dynamics |

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### Contents

Associated Actions and Uniqueness of Cocycles | 1 |

Koksmas Inequality and Group Extensions of Kronecker | 27 |

Normality to Different Bases | 51 |

Copyright | |

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### Common terms and phrases

a-equivalence action Algorithms assume automorphism billiards called ceiling function cocycle compact connected consider constant construction continued fractions continuous family continuous map converges Corollary countable curve cylinder flows define definition denote diffeomorphisms eigenvalue equation equivalence relation ergodic theory exists expansion Feller diffusion finite fixed point flow column Ford circle Fractals function geodesic flow height Hence Hofbauer homeomorphism hyperbolic implies induced inequality infinite inlet velocity interval invariant factor isomorphic Julia set Kakutani equivalence Lebesgue measure length level sets Markov partition Math Mathematics measure preserving metric n-block negative curvature non-singular normal to base Note obtain orbit equivalence path of homeomorphisms periodic point perturbation positive integer probability measure proof of Theorem Proposition prove recurrent resp Riemannian S-normality satisfying self-similar self-similar set semi-conjugacy maps sequence sets of Xi Sierpinski gasket skyscraper space subset Suppose symbolic dynamics Theorem 2.1 topological transformation unique