Mi hanno segnalato questo seminario domani al Centro De Giorgi --- non è uno della nostra serie, ma è comunque un argomento che può essere interessante per alcuni. Cordialmente,

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*From: *Paolo Giulietti <paologiulietti.math@gmail.com <mailto:paologiulietti.math@gmail.com>> *Subject: **[dynlist] Dyn.Sys - C. Wormell @ Centro De Giorgi 14,00h - 14th Nov.* *Date: *November 12, 2018 at 5:35:20 PM GMT+1 *To: *dynlist-pisa@googlegroups.com <mailto:dynlist-pisa@googlegroups.com>

Dear Dynamical Friends,

this week, on Wednesday 14th of November at 14:00h at the Centro de Giorgi, ground floor,  C. Wormell from the University of Sydney will talk about  "Chebyshev Galerkin methods for transfer operators in uniformly-expanding dynamics" (abstract below).

Let me Remind you that at 15:00h at Palazzo della Carovana there will be the monthly science colloquium of the SNS.

Moreover, if you are using the GoogleCalendar, check it out to see latest additions to the January/February  schedule!

Cheers! P&J

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Abstract: Full-branched expanding maps, a class of simple chaotic systems, are commonly used as models for chaotic dynamics, as well as being of number-theoretical interest. However, nonspecialised numerical methods to calculate long-time statistical quantities such as invariant measures have a poor trade-off between computational effort and accuracy.

In this talk I will present a rigorous method to calculate statistics of these maps by discretising the transfer operator in a Chebyshev polynomial basis. This is a highly efficient discretisation: I will show that, for analytic maps, numerical estimates obtained with this method converge exponentially quickly in the order of the discretisation. Finally, I will discuss some implementations of these algorithms for exploration and rigorous proof: in particular, in only a fraction of a second on a personal computer one can produce estimates of most statistical properties accurate to 14 decimal places.

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