The Hartman-Grobman Theorem, Structural Stability of Linearization, and Stable/Unstable Manifolds

This video explores a central result in dynamical systems: The Hartman-Grobman theorem. This theorem establishes when a fixed point of a nonlinear system will resemble its linearization. In particular, hyperbolic fixed points, where every eigenvalue has a non-zero real part, will be "structurally stable" so that the nonlinear system resembles its linearization in a neighborhood of the fixed point. We also discuss the existence of stable and unstable manifolds. Playlist: https://www.youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA Course Website: http://faculty.washington.edu/sbrunton/me564/ @eigensteve on Twitter eigensteve.com databookuw.com This video was produced at the University of Washington %%% CHAPTERS %%% 0:00 Hartman-Grobman and hyperbolic fixed points 10:36 Stable and unstable manifolds 13:50 Example of stable manifold