A hyperbolic \b[<sink fixed point of a map>] has both Jacobian <eigenvalues> strictly inside the <unit circle>. Its iterates locally attract nearby initial states; complex <fixed-point multipliers> can make the approach spiral. Zero <fixed-point multipliers> are strongly contracting and can occur for <noninvertible maps>. A <fixed-point multiplier> of modulus one requires nonlinear or exact analysis.

Solution

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

 Solution (source code)