Questions tagged [complex-dynamics]
Dynamics of holomorphic transformations; Mandelbrot and Julia sets.
204 questions
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Attractive Basins and Loops in Julia Sets
I recently learned about the Mandelbrot set for the first time from a presentation by some undergraduates in honor of Mandelbrot's death. The presentation was short and by non-experts so I left with ...
- 6,548
3
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3
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Analytic ODE with complex time
Suppose we have a complex vector field on $\mathbb{C}^n$ which is analytic and has $|DV| < L$ on ball $B_r$ with radius r.
I would like to understand:
1) if there exists an analytic flow $\phi_t(x)...
2
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1
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Help determining the asymptotic behavior of an integral involving rational functions.
Let $\phi:\mathbb{P}^1\to\mathbb{P}^1$ be a rational function of degree $d\geq2$. How can one prove, using the normalized spherical measure, that
$$\int_{\mathbb{P}^1(\mathbb{C})}|(\phi^n)'(z)|\ d\mu (...
- 11.8k
10
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What is the "category of bifurcations"?
While reading the introduction to this paper by Curtis McMullen, I came to the following (bold added):
In this paper we show that every bifurcation set contains a copy of the boundary of the ...
- 5,992