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Results tagged with ds.dynamical-systems
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user 18698
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.
10
votes
2
answers
470
views
When is every orbit closure uniquely ergodic?
Given a topological dynamical system $(X,T)$ (so that $T$ is a homeomorphism of the compact metric space $X$) and a point $x\in X$ we call the set ${\mathcal O}(x):=\overline{\{T^nx:n\in\mathbb Z\}}$ …
- 1,701
5
votes
Accepted
Are irrational multiples of central sets again central?
The answer is yes, it was pointed out to me by Vitaly Bergelson that it follows from Theorem 6.1 (d) of a paper by Bergelson, Hindman and Kra (Trans. Amer. Math. Soc. 348 (1996), no. 3, 893–912).
The …
- 1,701
1
vote
Density of a difference set of a set wih zero upper Banach density
Answering to the question formulated in the comments ("Is there a set $P$ with upper density $1$ such that $A-A$ is not contained in $P$ for any set $A$ with positive upper Banach density?"), note tha …
- 1,701