Geometry in the Neighborhood of Invariant Manifolds of Maps and Flows and Linearization (Pitman Research Notes in Mathematics Series,) by Urs Kirchgraber (PDF)

Description

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.

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