13.12.2018 | Yonatan Gutman | Introduction to Rokhlin and sofic entropy theories (II) |

6.12.2018 | Yonatan Gutman | Introduction to Rokhlin and sofic entropy theories (I) |

29.11.2018 | Adam Abrams | A survey of mathematical billiards and related systems |

22.11.2018 | Adam Śpiewak | Maximising Bernoulli measures and dimension gaps for countable branched systems |

15.11.2018 | Adam Abrams | Partitions arising from dynamics of complex continued fractions |

8.11.2018 | Reza Mohammadpour Bejargafsheh | Furstenberg's formula for Lyapunov exponents of linear cocycle (3) |

25.10.2018 | Reza Mohammadpour Bejargafsheh | Furstenberg's formula for Lyapunov exponents of linear cocycle (2) |

18.10.2018 | Artem Dudko | On resurgent approach to dynamics of parabolic germs (2) |

11.10.2018 | Reza Mohammadpour Bejargafsheh | Furstenberg's formula for Lyapunov exponents of linear cocycle (1) |

4.10.2018 | Artem Dudko | On resurgent approach to dynamics of parabolic germs (1) |

It is known since a paper by Kifer, Peres and Weiss that
dim(μ) is uniformly bounded away from 1 among all probability measures
μ on the unit interval which make the digits of the continued fraction
expansion i.i.d random variables. I will present a recent paper
*Maximising Bernoulli measures and dimension gaps for countable branched
systems* by Simon Baker and Natalia Jurga, where the authors prove that
there exists a measure maximising the dimension in this class. The
results are valid for a more general class of countable branched systems.

For real continued fractions, the natural extension of the Gauss map has a global attractor with "finite rectangular structure" owing to the "cycle property" satisfied by each algorithm. In this talk I will present a new property satisfied by a large variety of complex continued fraction algorithms and use it to explore the structure of bijectivity domains for natural extensions of complex Gauss maps. These domains can be given as a finite union of Cartesian products in $\mathbb C\times\mathbb C$, where in one complex coordinate the sets come from explicit manipulation of the algorithm, and in the other coordinate the sets are determined by experimental means.