Math 6410 • ODE

Consider a second order, linear autonomous system \(\dot{x}=Ax\), \(x\in\R^2\).
\begin{enumerate}
\item[(a)] Suppose that \(A\) has a pair of complex conjugate eigenvalues. By performing an
appropriate change of coordinates, convert the equation into Jordan normal form and thus
obtain the general solution.

\item[(b)] Under what conditions is the fixed point at the origin hyperbolic? Explain
the significance of hyperbolic fixed points in the theory of nonlinear ODEs.
\end{enumerate}