General relativity is a dynamical theory for the gravitational interaction formulated by A. Einstein in 1916. It postulates the existence of a dynamical spacetime which influences and is influenced by matter through the celebrated Einstein’s field equations. It revolutionised theoretical physics and introduced novel fields of study such as relativistic cosmology, gravitational waves, black holes, and other areas at the forefront of current research. It has also helped in the development of mathematics by contributing to such areas as Riemannian geometry, dynamical systems, and partial differential equations. It also plays an important role in experimental physics and observational astronomy.

Bifurcation theory introduced by H. Poincare may be defined as the field of mathematics devoted to the study of equations with multiple solutions. Another definition is to say that it provides the whole spectrum of possible instabilities which a physical system may possess or develop, and the possible ways in which the system may transfigure from one state to a different one. The standard approach to bifurcation theory is through dynamical systems, but more advanced approaches use singularity theory and catastrophe theory.

Although both fields, general relativity and bifurcation theory, have been developing intensely and largely independently for more than 100 years, it has recently become clear that many fundamental phenomena and properties of the former theory may in fact be described by methods of the latter. Indeed, the interface between the two is a new area of research in applied mathematics and theoretical physics. For more details, see my `Works’ page.