ABSTRACT

Catastrophe Theory was introduced in the 1960s by the renowned Fields Medal mathematician René Thom as a part of the general theory of local singularities. Since then it has found applications across many areas, including biology, economics, and chemical kinetics. By investigating the phenomena of bifurcation and chaos, Catastrophe Theory proved to

chapter Chapter 1|34 pages

Nondegenerate Critical Points: The Morse Lemma

chapter Chapter 2|22 pages

The Fold and the Cusp

chapter Chapter 3|8 pages

Degenerate Critical Points: The Reduction Lemma

chapter Chapter 4|48 pages

Determinacy

chapter Chapter 5|16 pages

Codimension

chapter Chapter 7|24 pages

Unfolclings

chapter Chapter 8|8 pages

Transversality

chapter Chapter 9|20 pages

The Malgrange—Mather Preparation Theorem

chapter Chapter 10|14 pages

The Fundamental Theorem on Universal Unfoldings

chapter Chapter 11|26 pages

Genericity

chapter Chapter 12|14 pages

Stability