Geometry in the Neighbourhood of Invariant Manifold of Maps and Flows and Linearization

The aim of this Research Note is to elucidate the behaviour of a dynamical system in the neighborhood of a fixed point or invariant torus (in the case of a diffeomorphism) or an equilibrium (in the case of an ordinary differential equation). It is shown that the space has both a horizontal and vertical foliation. Each leaf in the vertical foliation consists of the initial points of those orbits which are asymptotic to a particular orbit on the center-stable manifold. This structure leads to a linearization of the system.
Readership: Researchers and graduate students in a category theory, lattice theory, partially ordered algebraic structures, ideal theory, ring theory and theoretical computer science.