ON THE BIRTH OF ISOLAS.

Isolas are isolated, closed curves of solution branches of nonlinear problems. They have been observed to occur in the buckling of elastic shells, the equilibrium states of chemical reactors and other problems. A theory to describe analytically the structure of a class of isolas is presented. Specifically, isolas that shrink to a point as a parameter tau of the problem approaches a critical value tau //0 are considered. The point is referred to as an isola center. Equations that characterize the isola centers are given. Then solutions are constructed in a neighborhood of the isola centers by perturbation expansions in a small parameter epsilon that is proportional to ( tau minus tau //0)** alpha , with alpha appropriately determined. The theory is applied to a chemical reactor problem.