Existence of a Slow Manifold in a Model System of Equations

Abstract

A model system of equations proposed by Lorenz and Krishnamurthy is analyzed. The Hartman-Grobman theorem is employed to prove that the equations of the model admit a slow manifold devoid of gravity-wave activity, and the theory of normal forms is used to construct the manifold and to determine when the manifold is stable. The study disproves a conjecture by Lorenz and Krishnamurthy that a slow manifold does not exist for their model.