All Questions
7
questions
8
votes
1
answer
269
views
State of the art on: "If a dynamical system is Li-Yorke chaotic, does there exist a Cantor scrambled set?"
The following problem is presented in the paper Recent development of chaos theory in topological dynamics - by Jian Li and Xiangdong Ye :
"If a dynamical system [$(X,f)$, $X$ metric space, $f$ ...
- 149
18
votes
2
answers
1k
views
Existence of continuous map on real numbers with dense orbit?
Does there exist a continuous map $f:\mathbb{R}\rightarrow \mathbb{R}$ such that the forward orbit of 0 is dense in $\mathbb{R}$?
- 179
15
votes
1
answer
474
views
Group actions and "transfinite dynamics"
$\DeclareMathOperator\Sym{Sym}$I have a question about what I shall name here "transfinite dynamics" because it involves iterating a topological dynamical system $G \curvearrowright X$ ...
- 4,010
2
votes
1
answer
517
views
Is there a minimal, topologically mixing but not positively expansive dynamical system?
Is there a compact metric space $X$ and a function $f:X\to X$ such that the dynamical system $(X, f)$ has the following three properties?
minimal
topologically mixing (a map $f$ is topologically ...
- 83
6
votes
2
answers
581
views
Is there a topologically mixing and minimal homeomorphism on the circle (or on $\mathbb S^2$)?
The irrational rotation on the circle is both a homeomorphism and minimal but is not topologically mixing. The argument-doubling transformation on the circle is topologically mixing but is neither a ...
- 83
7
votes
1
answer
369
views
Approximation of topological dynamical systems?
I'm trying to find references to approximations of topological dynamical systems in the following sense:
A topological dynamical system $(X, f)$ consists of a topological space (typically compact ...
- 141
8
votes
1
answer
630
views
Is there a universal $\omega$-limit set?
For the purposes of this question, a dynamical system means a compact metric space $X$ together with a continuous map $f: X \to X$.
For $x \in X$, the $\omega$-limit set of $x$, denoted $\omega(x)$, ...
- 17.1k