All Questions
3 questions
19
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 $\mathbb{R}$?
- 189
6
votes
2
answers
729
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
2
votes
1
answer
592
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