All Questions
10 questions
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Holomorphic dynamical systems defined on a contractible bounded open subset of $\Bbb{C}^n$
Let $U$ be a contractible bounded open subset of $\Bbb{C}$. There is a standard classification of possible dynamical behaviors of holomorphic maps $f:U\rightarrow U$:
Attracting Case: There is an ...
- 3,599
1
vote
1
answer
486
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Mandelbrot set and logistic map connection
I'm currently writing an undergraduate thesis on chaos theory with a particular focus on the connection between the Mandelbrot set and the logistic map. I have found scattered posts on this site, ...
4
votes
1
answer
116
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Can iterates of a non-polynomial function be bounded by an exponential indefinitely?
Assume $f$ is an entire non-polynomial function of arbitrarily small exponential order ('zero'th order' if you're into calling it that). Is it possible that for all $n$ we have
$$|f^{\circ n}(z)| <...
user78249
6
votes
0
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223
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Reference request: Complex geodesic flow
Can someone suggest a book on complex geodesic flow? I am interested in it mainly because I was told these form a very useful class of Riemann surface laminations. Of special interest to me is the ...
3
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3
answers
1k
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reference on complex dynamics
Please someone suggest me some reference on the topic "Complex Dynamics". I want a brief geometric treatment from the root level. I have graduate level background on complex analysis, riemannian ...
24
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1
answer
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Anti-Mandelbrot set
I clearly remember seeing a paper where the dynamic of the anti-conformal map
$f(z)=\overline{z}^2+c$ was studied (the bar means complex conjugation). There was a picture of the analog of the ...
- 91.8k
12
votes
4
answers
988
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Rounding errors in images of Julia sets
One typically computes Julia sets by iterating a complex function, such as a polynomial or rational function.
How do rounding errors affect the results?
I'm looking for references on this issue, ...
- 3,022
1
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0
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226
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What is the state of the art of visualizing bifurcations for "difficult" dynamical systems?
This question is related to my other recent question on MO (although I am not confident that the dynamical system described in that other question is actually "difficult," in the sense that I will ...
- 709
3
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1
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Is there literature available on iterated function systems of the form $f^n = (g f^{n - 1}, g f^{n - 2}, \ldots)$?
This question is motivated by another question on math.stackexchange.
From a function $g:X^k\to X$ it is possible to define an iterated function system on $X^k$ with the function $f:X^k\to X^k$ ...
- 709
3
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0
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Question about a length inequality in algebraic dynamics
Let $X$ be a Noetherian scheme. Let $f\colon X\rightarrow X$ be an integral self-morphism. If $x\in X$ is a closed point, I will write $\mathcal{F}_{1}^x$ for the coherent sheaf of $\mathcal{O}_X$-...
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