The course teaches how to simplify nonlinear terms in autonomous vector fields with equilibrium points by introducing normal forms. Students will learn to determine categories of topological equivalence, simplify 2nd order terms, and apply normal form theory. The teaching method includes lectures and examples, with a focus on the Bogdanov-Takens normal form. This course is intended for individuals interested in dynamical systems, nonlinear dynamics, and applied mathematics.
Overview
Syllabus
Simplifying nonlinear terms and determining categories of topological equivalence.
1D example of simplifying a 1-dimensional ODE.
Normal form theory.
Simplifying the 2nd order terms.
Example of normal form for 2-dimensional vector field.
Takens normal form.
Bogdanov normal form.
Taught by
Ross Dynamics Lab
