At a differentiable <fixed point>, linear perturbations advance by the <Jacobian matrix>. A hyperbolic \b[<source fixed point of a map>] has both <eigenvalues> of modulus greater than one, so nearby perturbations expand under forward <iteration of a map>. Real signs can cause alternating directions and a complex pair can cause spiral expansion. <Eigenvalues> on the <unit circle> are excluded from this linear classification.

Solution

Past exam of the topics in applied mathematics course of the University of Oxford / 2007 / B / 7 / i / Solution

 Solution (source code)