25 research outputs found
On non-QRT Mappings of the Plane
We construct 9-parameter and 13-parameter dynamical systems of the plane
which map bi-quadratic curves to other bi-quadratic curves and return to the
original curve after two iterations. These generalize the QRT maps which map
each such curve to itself. The new families of maps include those that were
found as reductions of integrable lattices
Is the classical Bukhvostov-Lipatov model integrable? A Painlev\'e analysis
In this work we apply the Weiss, Tabor and Carnevale integrability criterion
(Painlev\'e analysis) to the classical version of the two dimensional
Bukhvostov-Lipatov model. We are led to the conclusion that the model is not
integrable classically, except at a trivial point where the theory can be
described in terms of two uncoupled sine-Gordon models
Singularity, complexity, and quasi--integrability of rational mappings
We investigate global properties of the mappings entering the description of
symmetries of integrable spin and vertex models, by exploiting their nature of
birational transformations of projective spaces. We give an algorithmic
analysis of the structure of invariants of such mappings. We discuss some
characteristic conditions for their (quasi)--integrability, and in particular
its links with their singularities (in the 2--plane). Finally, we describe some
of their properties {\it qua\/} dynamical systems, making contact with
Arnol'd's notion of complexity, and exemplify remarkable behaviours.Comment: Latex file. 17 pages. To appear in CM