Dynamical systems theory underpins our modern understanding of complex behaviours that arise in both natural and engineered systems. At its core, this field addresses the evolution of systems over ...

Chaotic dynamical systems are characterised by their inherent unpredictability and extreme sensitivity to initial conditions. This behaviour, often termed the “butterfly effect”, means that small ...

Introduces undergraduate students to chaotic dynamical systems. Topics include smooth and discrete dynamical systems, bifurcation theory, chaotic attractors, fractals, Lyapunov exponents, ...

In 1885, King Oscar II of Sweden announced a public challenge consisting of four mathematical problems. The French polymath Henri Poincaré focused on one related to the motion of celestial bodies, the ...