In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is … See more

Catastrophe theory analyzes degenerate critical points of the potential function — points where not just the first derivative, but one or more higher derivatives of the potential function are also zero. These are called the … See more

Catastrophe theory studies dynamical systems that describe the evolution of a state variable over time :
In the above equation, is referred to as the potential function, and is often a vector or a scalar whic… See more

Umbilic catastrophes are examples of corank 2 catastrophes. They can be observed in optics in the focal surfaces created by light reflecting off a surface in three dimensions and are intimately connected … See more

Vladimir Arnold gave the catastrophes the ADE classification, due to a deep connection with simple Lie groups.
• A0 - a non-singular point: .
• A1 - a local extremum, either a stable minimum or unstable m… See more