Graduate Seminar Report on the Hartman-Grobman Theorem and Planar Systems
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Date
2012-02
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Addis Ababa University
Abstract
The purpose of this study was to investigate the overall qualitative behavior of two
dimensional linear systems such as classification of the systems from the dynamical point
of view and in particular.
To obtain insight in the classification of fixed point using trace and determinant
of the coefficient matrix of planar systems;
To develop classification criteria using trace and determinant of the coefficient
matrix of the system, and also the way how to draw the trace determinant plane is
discussed.
To discuss the more subtle issue of topological equivalence (conjugacy) of these
systems. Starting from simple planar linear systems and then we develop insight
in investigating the relationship between two system that are topological
conjugate and equivalent.
Moreover, there is very important theorem mentioned in this project, the
Hartman-Grobman theorem, which results in the local behavior theory of
differential equations. The theorem shows near the hyperbolic fixed point, the
non-linear system has the same qualitative structure as its linearization
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Keywords
Hartman-Grobman Theorem and Planar Systems