Begin forwarded message:
*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
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.
--
"NO! Try not. Do, or do not. There is no try."
"Much to learn, you still have."
\Yoda\ smb://Yoda//
--
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