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Winter 2020, Math 367

Dynamics and Rigidity

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References

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Schedule

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Homework & Notes

The preliminary lecture notes below should be used with care; the notes are incomplete at the moment, several topics are missing. Please let me know if you spot any errors.

Dynamics and Rigidity

Time: |
Wednesday/Friday 1:30pm-2:50pm |

Location: |
Ryerson 358 |

NOTE | |

[Fr] | Furman - Random walks on groups and random transformations |

[EW] | Einsiedler, Ward - Ergodic Theory with a view towards Number Theory |

[MET] | Lectures on the Oseledets Multiplicative Ergodic Theorem |

The dynamics seminar meets on Mondays at 2:30pm, the schedule is here. |

Week | Topic |
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8 - 10 Jan | Introduction; Birkhoff & Kingman ergodic theorems |

15 - 17 Jan | Examples |

22 - 24 Jan | Factors, Furstenberg examples |

29 - 31 Jan | Hopf argument, Lyapunov exponents |

5 - 7 Feb | Positivity of top Lyapunov exponent |

12 - 14 Feb | Conditional expectation. More on random walks. |

19 - 21 Feb | Positivity and simplicity of top Lyapunov exponent |

26 - 28 Feb | Introduction to entropy |

4 - 6 Mar | Abelian dynamics on the circle |

11 - 13 Mar | Abelian dynamics on the space of lattices |

The preliminary lecture notes below should be used with care; the notes are incomplete at the moment, several topics are missing. Please let me know if you spot any errors.