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