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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.

Homework problems are at the end of the Lecture Notes.

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.

Homework problems are at the end of the Lecture Notes.