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MathGroup Archive 2004

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Re: tetrahedral Siegel Disk Julia map

  • To: mathgroup at
  • Subject: [mg52413] Re: tetrahedral Siegel Disk Julia map
  • From: Roger Bagula <tftn at>
  • Date: Fri, 26 Nov 2004 01:04:49 -0500 (EST)
  • References: <co4ebr$lbo$>
  • Reply-to: tftn at
  • Sender: owner-wri-mathgroup at

A gallery of tetrahedral / K3 Siegel disk dynamics by Dr McMullen

        Dynamics on K3 surfaces

K3 movie <>
K3 surface <>
Tame <>
Wilder <>
Ergodic <>
Stable manifold 
Tame blowup 
Poncelet's theorem 
Poncelet Java 
(Schwartz) <>
Dynamics on a (2,2) curve 

Roger Bagula wrote:

>Siegel disks don't just happen in complex dynamics of quadratics.
>You can set this type of "motion" going on other Riemannian surfaces
>as Dr. McMullen suggested in his paper on K3 surfaces
>using an tetraheral implicit surface and a Salem based irrational number.
>In this simulation an Siegel disk is located on a Riemannian
>tetraheral surface.
>(*tetrahedral Siegel Disk Julia map*)
>(* idea based on McMullen K3 ( tetrahedral) surface Siegel disk dynamics*)
>(* Riemannian Tetrahedron polynomial from Elliptic Curves, McKean and Moll,
>  p22, Ellipical invariants of Platonic solids*)
>(* j[z]=(z^4-2*Sqrt[3]*I*z^2+1)^3/(z^4+2*Sqrt[3]*I*z^2+1)  *)
>a=Flatten[Table[Table[{x[n,t],y[n,t]},{n,0, digits}],{t,1,10}],1];
>ListPlot[a, PlotRange->All]
>Respectfully, Roger L. Bagula
>tftn at, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
>alternative email: rlbtftn at
>URL :

Respectfully, Roger L. Bagula
tftn at, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn at

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