SMS scnews item created by Zhou Zhang at Tue 21 Aug 2012 1521
Type: Seminar
Distribution: World
Expiry: 18 Sep 2012
Calendar1: 24 Aug 2012 1430-1530
CalLoc1: OMB-150, Old Main Building (UNSW)
Auth: zhangou@bari.maths.usyd.edu.au

# SYD-UNSW Joint Colloquium: Viallet -- Discrete-time Dynamical System: Integrable Or Not Integrable?

Speaker: Prof. Claude Viallet (LPTHE)

http://www.lpthe.jussieu.fr/~viallet/

Time: Friday, Aug. 24, 2:30--3:30PM

Room: OMB-150, Old Main Building (UNSW)

Lunch with speaker: we meet around 1PM at the entrance to the East Wing
of Red Centre Building.

One choice of commuting from Sydney: meet at Carslaw 620 around 12:25PM
and share taxi to UNSW. The round trip is covered by school colloquium
fund.

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Title: Discrete-time Dynamical System: Integrable Or Not Integrable?

Abstract: to any discrete-time dynamical system with a rational evolution,
it is possible to associate  a number, the "algebraic entropy", which is
a global index of complexity of the system.

Its vanishing is the hallmark of integrability, and it proved to be an
unsurpassed detector of integrability.  But it is also an interesting
object in itself. Its analysis links in particular to algebraic
geometry and number theory.

We will give the definition of the entropy, and show on simple examples
how it can be calculated. We will then explain the link between this
concept and the singularity structure of the system, relating it to the
discrete Painlev\’e analysis (this is where algebraic geometry comes in).
We finally describe, in a simple case, the set of values assumed by the
entropy (this is where number theory enters, as it is conjectured to
always be the logarithm of an algebraic integer), and introduce the
notion of entropy gap.

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Joint Colloquium web site:

http://www.maths.usyd.edu.au/u/SemConf/JointColloquium/index.html


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