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Results tagged with complex-dynamics
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user 6129
Dynamics of holomorphic transformations; Mandelbrot and Julia sets.
5
votes
0
answers
102
views
wild julia sets
Using the Baire category theorem, we may show that most simple closed curves satisfy the following property: any segment between an interior point and an exterior point of the curve intersects the cur …
- 18.7k
4
votes
2
answers
331
views
Newton method and Siegel disks
I am looking for a degree 3 polynomial $P$ whose associated Newton's method $z \mapsto z - P(z)/P'(z)$ has a Siegel disk. Is there an explicit example of such polynomial $P$?
- 18.7k
15
votes
3
answers
1k
views
Convergence of Newton's method
For a polynomial $P$ of degree $n$ with real coefficients and with $n$ distinct real roots, the Newton's method $z_{n+1} = z_n - {P(z_n) \over P'(z_n)}$ converges for almost all initial values $z_0$ i …
- 18.7k