Questions tagged [ds.dynamical-systems]
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory, topological dynamics.
8 questions from the last 30 days
8
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1
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623
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Do all primes $>2$ hit $5$?
$2$ is a fixed point of the iteration:
$$q_{n+1}:=\min_{p|(q_n-1)^2+1} p$$
Start with $q_1>2$ prime. Does this iteration hit $5$? (min runs over primes)
- 3,761
7
votes
1
answer
697
views
Does the airplane Julia set contain true circles?
The well known "airplane" Julia set looks like it contains a true circle. To be precise, let $c$ be the real root of $x^3+2x^2+x+1=0$. i.e., $c\approx -1.75$. The Julia set of $z^2+c$ is the ...
- 105
2
votes
2
answers
264
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What literature can I read about the Janibekov effect and the intermediate axis theorem?
I have been studying mathematics for 2 years, and I have already read Terence Tao's publication. Please suggest books on related topics, such as Euler's equations, mathematical modeling, mathematical ...
- 33
2
votes
1
answer
411
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Unprovable statements and generic properties
I should start with the following disclaimer that I know virtually no logic, sorry forgive me if my questions are ill-posed. I appreciate that all of this is probably completely obvious to a logician, ...
- 3,108
5
votes
1
answer
122
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Possible asymptotic behavior of recurrence function
I was wondering and tried to find what are the results known related to recurrence function of a minimal subshift $\Omega \subseteq A^{\mathbb{Z}}$, where $A$ is finite non empty subset.
If I am not ...
- 755
1
vote
1
answer
203
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Book recommendation for smooth ergodic theory
I'm interested in smooth ergodic theory.
Please teach me some recommended books for it.
Actually, now I have been reading the supplement of Katok's book, Introduction to the Modern Theory of Dynamical ...
- 81
6
votes
0
answers
144
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Ergodicity in the Wiener-Wintner Ergodic Theorem [cross-post from MSE]
I'm studying the Wiener-Wintner (and related) ergodic theorems, and I've been running into a bit of confussion when passing the result from ergodic systems to non-ergodic ones. In most of the ...
- 61
1
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0
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57
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Dynamics of the arithmetic–derivative family $f_k(n)=n+k(D(n)-1)$
Let $D(n)$ be the arithmetic derivative, defined by: $D(p)=1$ for primes $p$, $D(ab)=D(a)b+aD(b).$
For a fixed integer $k$, consider the dynamical system
$$f_k(n)=n+k(D(n)−1).$$
I am interested in the ...
- 1,018