## Computational Ergodic TheoryErgodic theory is hard to study because it is based on measure theory, which is a technically difficult subject to master for ordinary students, especially for physics majors. Many of the examples are introduced from a different perspective than in other books and theoretical ideas can be gradually absorbed while doing computer experiments. Theoretically less prepared students can appreciate the deep theorems by doing various simulations. The computer experiments are simple but they have close ties with theoretical implications. Even the researchers in the field can benefit by checking their conjectures, which might have been regarded as unrealistic to be programmed easily, against numerical output using some of the ideas in the book. One last remark: The last chapter explains the relation between entropy and data compression, which belongs to information theory and not to ergodic theory. It will help students to gain an understanding of the digital technology that has shaped the modern information society. |

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### Contents

tents | 1 |

Z Measures and Lebesgue Integration | 7 |

Compact Abelian Groups and Characters | 14 |

Continued Fractions | 20 |

variant Measures | 47 |

Isomorphic Transformations | 61 |

he Birkhoff Ergodic Theorem | 85 |

Gelfands Problem | 99 |

Z Number of Signiﬁcant Digits and the Divergence Speed | 279 |

Speed of Approximation by Convergents | 287 |

Multidimensional Case | 299 |

The Lyapunov Exponent of a Differentiable Mapping | 311 |

able and Unstable Manifolds | 333 |

The Standard Mapping | 339 |

Maple Programs | 345 |

ecurrence and Entropy | 363 |

Maple Programs | 113 |

he Central Limit Theorem | 133 |

Speed of Correlation Decay | 143 |

Iore on Ergodicity | 155 |

How to Sketch a Conjugacy Using Rotation Number | 195 |

Uniform Distribution | 211 |

Mod 2 Normality Conditions | 219 |

How to Sketch a Cobounding Function | 227 |

148 | 241 |

OneDimensional Case | 270 |

153 | 276 |