- uniform generators and symbolic extensions in low dimensions;
- rate of convergence of the tail entropy for $C^\infty$ smooth systems;
- equidistribution of periodic points with lower bounded Lyapunov exponents along measure of maximal entropy in low dimensions.

- Definitions of Dimension (Box, Hausdorff, Fourier);
- Potential and measures;
- Iterated function schemes and expanding maps;
- Conformal maps and repellers;
- Examples: Julia sets and Schottky group limit sets;
- Bedford-McMullen Carpets.

- Pressure and Bowen-Formula;
- Analyticity of pressure;
- Numerical approximation of dimension;
- The McMullen approach;
- The determinant approach;
- Multi fractal analysis.

- Transversality;
- Differences of Cantor sets;
- $\{0,1,3\}$-sets;
- Bernoulli convolutions;
- Absolute continuity;
- Exceptional sets;
- (Fourier dimension).

- Furstenberg's viewpoint;
- Scenary flow;
- Microsets and Measures.

Time | Title | Place |
---|---|---|

09.00-09.55 | Registration | Jabir ibn Hayyan Hall |

Time | Lecturer | Title |
---|---|---|

10.00-11.10 | Mark Pollicott | Dimension and Dynamics (Background) |

11.10-11.30 | Coffee Break | |

11.30-12.40 | David Burguet | Entropy of $C^r$, $r>1$, smooth systems via semi-algebraic tools (I) |

12.40- 14.00 | Lunch | |

14.00-15.30 | Mark Pollicott Exercise I | |

15.30-16.00 | Coffee Break | |

16.00-17.30 | David Burguet Exercise I |

Time | Lecturer | Title |
---|---|---|

10.00-11.10 | Mark Pollicott | Thermodynamic viewpoint and computation |

11.10-11.30 | Coffee Break | |

11.30-12.40 | David Burguet | Entropy of $C^r$, $r>1$, smooth systems via semi-algebraic tools (II) |

12.40- 14.00 | Lunch | |

14.00-15.30 | Mark Pollicott Exercise II | |

15.30-16.00 | Coffee Break | |

16.00-17.30 | David Burguet Exercise II |

Time | Lecturer | Title |
---|---|---|

10.00-11.10 | Mark Pollicott | Transversality |

11.10-11.30 | Coffee Break | |

11.30-12.40 | David Burguet | Entropy of $C^r$, $r>1$, smooth systems via semi-algebraic tools (III) |

12.40- 14.00 | Lunch | |

14.00-15.30 | Mark Pollicott Exercise III | |

15.30-16.00 | Coffee Break | |

16.00-17.30 | Mark Pollicott Talk at IPM |

Time | Lecturer | Title |
---|---|---|

10.00-11.10 | Mark Pollicott | Microsets and Scenery flow |

11.10-11.30 | Coffee Break | |

11.30-12.40 | David Burguet | Entropy of $C^r$, $r>1$, smooth systems via semi-algebraic tools (IV) |

12.40- 14.00 | Lunch | |

14.00-15.30 | Mark Pollicott Exercise IV | |

15.30-16.00 | Coffee Break | |

16.00-17.30 | David Burguet Exercise III |

Time | Lecturer | Title |
---|---|---|

10.00-11.10 | Mark Pollicott Talk at seminar section | Validated Numerics-Computing the dimension of $E2$ to 100 decimal places |

11.10-11.30 | Coffee Break | |

11.30-12.40 | David Burguet Talk at seminar section | TBA |

12.40- 14.00 | Lunch |

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