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Course syllabus.
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Homework (contains some notes from class and FractalStream scripts)
One of our favorite solutions to hw problem (72)
Programs
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FractalStream.
Mandel.
DE tool.
Xaos.
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References.
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Riemann surfaces,
dynamics and geometry by C. McMullen.
The Road To Chaos by R.
D. Neidinger and R. John Annen.
The Mandelbrot set is Universal by C. McMullen.
On iterated maps of the interval by J. Milnor and W. Thurston.
Entropy in dimension One by W. Thurston.
David's references: Online Encyclopedia of integer sequences, Simple mathematical models with very complicated dynamics, On finite limit sets for transformations of the unit
interval, The cycle enumerator of unimodal permutations, On the
bifurcation of maps of the interval,
Periodic orbits and kneading invariants, Geneaology of periodic
orbits of maps of the interval
Period three implies chaos
An earlier version of Milnor's dynamics book
The polynomials associated with a Julia set
Disconnected Julia sets
A primer on mapping class groups, by Farb and
Margalit.
Thurston equivalence of topological polynomials (aka the paper
that solves the twisted rabbit
problem), by Bartholdi and Nekrashevych
A proof by picture of the Perron-Frobenius Theorem, by Aaron Fenyes.
Pasting together Julia sets: a worked
out example of mating, by John Milnor.
A proof of Thurston's topological
characterization of rational functions, by Adrien Douady and John H. Hubbard.
A family of cubic
rational maps and matings of cubic polynomials, by Tan Lei and Mitsu Shishikura.
Tan Lei and Shishikura's example of
non-mateable degree 3 polynomials without a
Levy cycle, by Arnaud Cheritat. His slides are
here.
Here is a link to
Arnaud Cheritat's website about polynomial matings.
Quadratic matings and ray
connections, by Wolf Jung.
Questions about polynomial matings, by X. Buff, A. Epstein, S. Koch, D. Meyer, K. Pilgrim, M. Rees,
and Tan Lei
On Lattes Maps, by J. Milnor
Finite dimensional Teichmueller spaces and generalizations, by L. Bers
Algorithms for computing angles in the Mandelbrot set, by A. Douady
Kevin's notes from the workshop - thanks Kevin!
A positive characterization of rational maps, by D. Thurston
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