DEEPER ANALYSIS
OF THE ASTRO-MATHEMATICAL PUZZLE
The Complex Universe has connections to many areas of
mathematics. For instance, Banach's contraction principle
inspires us to study the stability of the attractors (e.g.,
centers of galaxies), and to see how close they are to
`explosion'. The number m of spiral arms can be
computed with such analysis, as well as the pitch angle
of arms, but so far only for the non-clustered objects.
There must be rich connections to the world
of fractals, dynamical systems,
..., ...., .... (please fill in the blanks).
A hypothesis remains to be verified,
saying that the number of objects into which
a galaxy `bursts' on crossing the critical z
equals the number of arms in that galaxy.
Much of the analysis is to be performed/described.
Below I will outline just some interesting zero-order results:
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