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Results tagged with ds.dynamical-systems
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user 172802
Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.
6
votes
Accepted
Boundedness of orbits and limit sets
We can modify the connectedness argument to show it also holds for homeomorphisms: suppose $\omega(x)$ is contained in an open ball $B(0,R)$, with $R>0$, and let $N$ be so big that $T(B(0,R))\subseteq …
- 10.6k
2
votes
Accepted
First visit of intervals for an irrational rotation
No, it is not possible. In the following I will use $I_n=(a_n,b_n)$ instead of $[a_n,b_n)$ (this is not a problem, you can just increase $a_n$ a bit so that the statement with $I_n=(a_n,b_n)$ is stron …
- 10.6k
3
votes
1
answer
120
views
Do sets of big returns contain sets of returns?
We say a subset $E$ of $\mathbb{N}$ is a set of returns if there is some measure preserving system $(X,\mathcal{B},\mu,T)$ and some $A\in\mathcal{B}$ with $\mu(A)>0$ such that $E=\{n\in\mathbb{N};\mu( …
- 10.6k