# Index of /~cheritat/MatMovies

Parent Directory  -
AirplaneDendrite/10-Jun-2007 19:33 -
AirplanePrim4/13-Jun-2007 13:58 -
AirplaneRabbit/12-Oct-2007 10:34 -
Bug/20-Jun-2007 11:39 -
Deg3Newton/05-Mar-2009 22:01 -
Den_1_6_Den_5_14/05-Jun-2007 23:57 -
DendriteDendrite/12-Oct-2007 10:26 -
DendriteOtherdendrite/12-Oct-2007 10:21 -
DendriteRabbit/12-Oct-2007 10:20 -
Magic/14-Apr-2012 16:19 -
RabbitBasilica/12-Oct-2007 00:02 -
RabbitPrim4/12-Oct-2007 10:35 -
RabbitRabbit/24-Feb-2009 14:23 -
ReesSharedExample/12-Oct-2007 00:11 -
Siegels/12-Oct-2007 10:40 -
Tuning/23-Feb-2008 14:25 -

# Polynomial matings on the Riemann sphere

Welcome. I did not work out thumbnails yet. Here's a little guide throughout the directory structure of MatMovies.

You'll find in these directories various animations. You may like to browse them according to the following list.

Ray numbers: they indicate the argument of external rays tending to the parameter in the Miziurewicz case ( <=> strictly preperiodic critical point => subhyperbolic polynomial and dendrite Julia set). In the hyperbolic case ( <=> periodic critical point => Julia set enclosing bounded components of Fatou set ) there are two external rays indicated, and they land not on the parameter but on another one, which is the root of the hyperbolic component containing the correct parameter.
• RabbitBasilica = mating of Douady's rabbit (ray=1/7 and 2/7) with the basilica (ray=1/3 and 2/3). The original example of mating.
• RabbitRabbit = mating of Douady's rabbit (ray=1/7 and 2/7) with another Douady's rabbit.
• RabbitPrim4 = mating of the Rabbit (1/7,2/7) with a period 4 primitive example in the 1/3 limb (ray=3/15 and 4/15).
• AirplaneRabbit = the Airplane (3/7,4/7) with the rabbit (1/7,2/7). This one has longer ray connexions, leading to a limit where it is hard to recognize the two original Julia sets.
• DendriteDendrite = a miziurewicz (ray=1/4) mated with an identical copy (ray=1/4 again). The limit is a Lattes example, it has a "regular" invariant measure (it is kind of evenly distributed) and is moreover related to the dragon area filling fractal curve. This is an example of Milnor.
• DendriteOtherdendrite If one mates 1/4 with 1/6 instead, the limit looks much less regular.
• DendriteRabbit = The 1/6 Mizurewicz with (1/7,2/7).
• AirplanePrim4 = Airplaine (3/7,4/7) with period 4 primitive copy in the 1/3 limb (3/15,4/15). See how intricate this gets. This is another example of shared mating.
• ReesSharedExamples = an example of shared matings.
• Deg3Newton = Mating two particular degree 3 polynomials leads to the Julia set of a Newton method of another degree 3 polynomial (communicated by Tan Lei).
• Siegels = Mating Siegel disks.
• Tunings = Polynomial tuning is a close relative of polynomial mating.
• ...