Geometry of Dynamical Systems

Abstract

In this thesis, we look into various aspects of local and global theory of Dynamical Systems. We primarily employ the stable manifold theorem and the Hartman-Grobman theorem. Using these theorems we have determined the qualitative structure of non-linear systems. We have studied the type and the behaviour of hyperbolic and non-hyperbolic critical points of non-linear systems. The stability of the periodic orbits is also determined by the various concepts of dynamical systems thoroughly.