Hyperbolic vs Non-Hyperbolic Fixed Points - Computing Their Invariant Manifolds via Taylor Series

This course focuses on understanding hyperbolic and non-hyperbolic fixed points in dynamical systems and computing their invariant manifolds using a Taylor series approach. The learning outcomes include grasping the concepts of stable, unstable, and center subspaces, distinguishing between linear subspaces and nonlinear invariant manifolds, and analyzing the significance of center manifold theory. Students will develop skills in calculating invariant manifolds analytically in a 2D example and approximating them through Taylor series expansion. The teaching method involves theoretical explanations, visual aids, and practical examples. This course is intended for individuals with a background in elementary analysis, multivariable calculus, linear algebra, and ordinary differential equations from a geometric perspective.