Mathematica code supplementary to a bachelor’s thesis on Feigenbaum scaling
The code generates all diagrams that can be found in figures.
It also computes the spectrum of the linearized period-doublding operater and the Feigenvalues via the direct method.
The file getFeigenbaum.wl is a package and needs to be included in a directory contained in $PATH
The following files are present:
CobwebPlot.nb - creation of the cobweb plots
Feigenbaum Scaling.pdf - the written presentation of the thesis
Feigenvalues.nb - computation of the generalized Feigenvalues and a plot of the superstable fixed-point equation
FinalStateDiagram.nb - creation of all final-state diagrams
getFeigenbaum.wl - computation of the Feigenvalues via the direct method
OrbitDistribution.nb - histragram plot at the Feigenbaum point and the end point
Plot3D.nb - 3D-Plot of f(mu,x)
PoincarePlot.nb - Poincare plot of f
SchwarzianDerivative.nb - plot of the Schwarzian derivative of f
SelfSimilarity.nb - all plots involving the self-similarity of the graph of f to higher iterates
Spectrum.nb - computation of the spectrum of the linearized period-doubling operator
UniversalFunction.nb - plots of the sequence {g_r} which converges to the universal function
Version 12.0.0.0 of Mathematica was used