All Questions
3
questions
6
votes
2
answers
388
views
Do mixing homeomorphisms on continua have positive entropy?
I am trying to understand relations between various measures of topological complexity. I have read that expansive homeomorphisms on continua, for example, have positive entropy. But I do not know ...
- 2,993
10
votes
1
answer
202
views
homeomorphisms induced by composant rotations in the solenoid
Let $S$ be the dyadic solenoid.
Let $x\in S$, and let $X$ be the union of all arcs (homeomorphic copies of $[0,1]$) in $S$ containing $x$.
$X$ is called a composant of $S$.
It is well-known ...
- 945
6
votes
1
answer
413
views
Transitive homeomorphisms of Erdős spaces
A surjective homeomorphism $h:X\to X$ is minimal if $$\overline{\{h^n(x):n\in \mathbb N\}}=X$$ for every $x\in X$. In other words, the orbit of each point is dense.
Does either of the Erdös spaces $\...
- 2,993