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Results tagged with ds.dynamical-systems
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user 28104
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.
13
votes
Accepted
A question on Collatz's conjecture:proportion of "low flying" orbits
If the sequence $(T(N))_{N \in \mathbb{N}}$ converges and the limit is
not equal to $0$, this would imply either positive predecessor density for $1$, cf. e.g.
Günther J. Wirsching, On the problem of …
- 19.6k
30
votes
2
answers
2k
views
Fractal-like structures arising from the action of a group on $\mathbb{Z}^2$
Let $G := \langle a, b, c \rangle < {\rm Sym}(\mathbb{Z}^2)$ be the group
generated by the permutation
$$
a: \ (m,n) \ \mapsto \ (m-n,m)
$$
of order $6$ and the involutions
$$
b: \ (m,n) \ \mapsto …
- 19.6k
16
votes
1
answer
1k
views
Are the algebraic numbers dense everywhere on the boundary of the Mandelbrot set?
Let $\mathcal{B}$ denote the boundary of the Mandelbrot set, and let
$\overline{\mathbb{Q}}$ denote the algebraic closure of the rationals.
Further put $\mathcal{B}_{\overline{\mathbb{Q}}} := \mathcal …
- 19.6k