Graduate Seminar Report On The Hartman-grobman Theorem And Planar Systems

The purpose of this study was to investigate the overall qualitative behavior of tworndimensional linear systems such as classification of the systems from the dynamical pointrnof view and in particular.rnTo obtain insight in the classification of fixed point using trace and determinantrnof the coefficient matrix of planar systems;rnTo develop classification criteria using trace and determinant of the coefficientrnmatrix of the system, and also the way how to draw the trace determinant plane isrndiscussed.rnTo discuss the more subtle issue of topological equivalence (conjugacy) of thesernsystems. Starting from simple planar linear systems and then we develop insightrnin investigating the relationship between two system that are topologicalrnconjugate and equivalent.rnMoreover, there is very important theorem mentioned in this project, thernHartman-Grobman theorem, which results in the local behavior theory ofrndifferential equations. The theorem shows near the hyperbolic fixed point, thernnon-linear system has the same qualitative structure as its linearization

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