Скачать или смотреть 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.

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This video was produced at the University of Washington

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0:00 Hartman-Grobman and hyperbolic fixed points
10:36 Stable and unstable manifolds
13:50 Example of stable manifold