Home work 6

Part I (Quantifying chaos)

Again let us look at our old friend the logistic equation, and let's pick the parameter as large as possible, i.e. study

Find (an approximation) of the Lyapunov exponent for this one dimensionally system.

Part II (Complex Dynamics)

a) Prove that any Möbius map can be written as a composition of translations, inversions, and homothetic transformations (i.e. z is transformed
to bz, for a complex valued b).

b) Describe the Julia set of this map: