Global Behaviour of Integrable Complex Systems. Complex systems as diverse as the weather and the solar system are modelled by non-linear equations that have elusive, unstable solutions. An infinitesimally small change in the state of the system at one place can lead to a vast change in its behaviour far away. Such extreme sensitivity is often take to be a sign of chaos, but it also occurs in completely ordered, integrable systems. Our main aim is to tackle the immense challenge of describing th ....Global Behaviour of Integrable Complex Systems. Complex systems as diverse as the weather and the solar system are modelled by non-linear equations that have elusive, unstable solutions. An infinitesimally small change in the state of the system at one place can lead to a vast change in its behaviour far away. Such extreme sensitivity is often take to be a sign of chaos, but it also occurs in completely ordered, integrable systems. Our main aim is to tackle the immense challenge of describing the global behaviour of such elusive solutions, particularly when the systems depend on many variables.Read moreRead less
Signatures of Order, Chaos and Symmetry in Algebraic Dynamics. The project in the breakthrough science of algebraic dynamics will help inform and sustain both algebraic number theory and dynamical systems in Australia. Thus far, Australia is not well represented in this cutting edge international area, and international research prominence and teaching benefits will flow from the pioneering and innovative topics to be addressed. The research incorporates the synergy of an existing highly-product ....Signatures of Order, Chaos and Symmetry in Algebraic Dynamics. The project in the breakthrough science of algebraic dynamics will help inform and sustain both algebraic number theory and dynamical systems in Australia. Thus far, Australia is not well represented in this cutting edge international area, and international research prominence and teaching benefits will flow from the pioneering and innovative topics to be addressed. The research incorporates the synergy of an existing highly-productive international collaboration and creates possibilities for many more such linkages. It affords Australia a strategic opportunity to considerably increase its profile in the algebraic dynamics community, particularly in the Pacific region.Read moreRead less