Preface Special issue in honor of Reinout Quispel

Abstract

Reinout Quispel was born on 8 October 1953 in Bilthoven, a small town near Utrecht in the Netherlands. He studied both chemistry and physics, gaining bachelor’s degrees at the University of Utrecht in 1973 and 1976 respectively, and then specialized in theoretical physics, with a Master’s degree in 1979 (on solitons in the Heisenberg spin chain, supervised by Theodorus Ruijgrok) and a PhD, Linear Integral Equations and Soliton Systems [22], in 1983, supervised by Hans Capel. This thesis, which begins with a study of integrable PDEs, arrives in Chapter 4 (later published in [24]) with the discovery of a method for obtaining fully discrete integrable systems on square lattices, that have as continuum limits the Korteweg–de Vries, nonlinear Schrödinger, and complex sine–Gordon equations, and the Heisenberg spin chain. Thus several of Reinout’s lifelong research interests – continuous and discrete integrability, and the relationship between the continuous and the discrete – were present right from the start. The next stop was a postdoc at Twente University, working with Robert Helleman, the founder of the ‘Dynamics Days’ conference series, before a long-distance move to the Australian National University, working with Rodney Baxter. Reinout and Nel expected this southern sojourn to last for three years; thirty-three years later they are still happily resident in Australia. In 1990 Reinout moved to La Trobe University, Melbourne, where he became a Professor in 2004. Reinout’s three main research areas are discrete integrable systems, dynamical systems, and geometric numerical integration, along with interactions between these topics. In discrete integrable systems, having introduced a major new direction in his PhD thesis – his novel reductions to Painlevé equations led to the Clarkson–Kruskal non-classical reduction method – he continued by codiscovering the QRT map [25, 26], an 18-parameter family of completely integrable maps of the plane. These turned out to have far-reaching implications in dynamical systems theory, geometry, and integrability. For example, the modern construction of nonautonomous dynamical systems known as discrete Painlevé equations rely on them. Their geometry is explored at length in the 2010 book QRT and Elliptic Surfaces by Hans Duistermaat and is still being investigated today. In dynamical systems, his work has centred on systems with discrete and/or continuous symmetries. His review [28] marked the emergence of reversible dynamical