# Dynamical Systems Learning Seminar

Thursdays, 15.15, room 408

 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)

## ABSTRACTS

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.