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Results tagged with complex-dynamics
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user 11260
Dynamics of holomorphic transformations; Mandelbrot and Julia sets.
21
votes
Is the area of the Mandelbrot set known?
New Approximations for the Area of the Mandelbrot Set gives the state of the art from 2014, and a related paper from 2015 is On a numerical approximation of the boundary structure and of the area of t …
- 188k
9
votes
Renormalization in physics vs. dynamical systems
The renormalization approach to dynamical systems pioneered by Chen, Goldenfeld and Oono [1] applies the Gell-Mann and Low renormalization group from quantum physics [2] to extract the global behavior …
- 188k
13
votes
Exponential towers of $i$'s
The single-valued case of the exponential tower of $i$ was studied by Peter Lynch. The tower converges along three spirals to the fixed point $Q=i^Q$, given in terms of the Lambert W-function by
$$Q= …
- 188k
6
votes
Precise location of the Mandelbrot Bulb Attachment to the main Cardioid
in the parameterization where the main cardioid is a circle, the bulbs are attached at rational angles $\phi=2\pi m/n$: see R.L. Devaney, The Mandelbrot bulbs.
- 188k