Dynamics with complex Eigenvalues

Due by Mon, 16 Apr 2018

Please do not submit this assignment. This is to only help with understanding the material on ODEs. It is not a model for final examination questions.

Let $A : \mathbb{R}^2 \to \mathbb{R}^2$ be a linear transformation. We can also regard this as a linear transformation $A : \mathbb{C}^2 \to \mathbb{C}^2$.

Assume henceforth that $A$ has complex eigenvalues $\alpha \pm i\beta$ for $\alpha, \beta \in\mathbb{R}$ with $\beta\neq 0$.

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