Title: The reversing symmetry group of planar polynomial automorphisms.

Speaker: John Roberts, La Trobe University, Melbourne, Australia

Abstract:

Certain dynamical systems (automorphisms) form algebraic groups with
a known group structure. We have recently followed a programme to
study the so-called reversing symmetry groups in such groups of
dynamical systems. The reversing symmetry group $R(g)$ of an element
$g$ comprises all elements that conjugate the element to $g$ or to its
inverse. Identifying $R(g)$ is helpful for revealing symmetries in
the dynamics of $g$.
Previously, we have identified $R(g)$ when $g$ belongs to the matrix groups
$GL(2,Z)$ and $SL(2,Z)$ (and their projective counterparts). In this
talk, we describe our latest results on the nature of $R(g)$ when $g$
belongs to the group of polynomial automorphisms of $R^2$ or $C^2$.
We make extensive use of the algebraic consequences of this group
having an amalgamated free product structure.