Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Transition systems

Konstantin Mischaikowa1

a1 Department of Mathematics, Michigan State University, East Lansing, MI 48824, U.S.A


The concept of a transition system is extended to a parametrised family of differential equations


where x ∊ ℝn and λ ∊ Λ = [0, l]m, an m-cube. Furthermore, algebraic formulae for comparing connection matrices at the various parameter values are obtained. Finally, several applications of these techniques are indicated.

(Received May 13 1988)

(Revised December 12 1988)