GCOE Seminars

Seminar information archive ~06/07Next seminarFuture seminars 06/08~


15:30-17:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Alfred Ramani (Ecole Polytechnique)
Linearisable mappings (ENGLISH)
[ Abstract ]
We present a series of results on linearisable second-order mappings.
Three distinct families of such mappings do exist: projective, mappings of Gambier type and mappings which we have dubbed "of third kind".
Our starting point are the linearisable mappings belonging to the QRT family. We show how they can be linearised and how in some cases their explicit solution can be constructed. We discuss also the growth property of these mappings, a property intimately related to linearisability.
In the second part of the talk we address the question of the extension of these mappings to a non-autonomous form.
We show that the QRT invariant can also be extended (to a quantity which depends explicitly on the independent variable). Using this non-autonomous form we show that it is possible to construct the explicit solution of all third-kind mappings. We discuss also the relation of mappings of the third kind to Gambier-type mappings. We show that a large subclass of third-kind mappings can be considered as the discrete derivative of Gambier-type ones.