network profile
| bio | website | |
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| location | ||
| age | ||
| visits | member for | 1 year, 1 month |
| seen | Apr 7 '12 at 17:58 | |
| stats | profile views | 4 |
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Apr 7 |
comment |
Having trouble understanding the concept of “mixing” in dynamical systems. OK, I see your point. Now that I think about, it's obvious that the limit won't exist for any bounded state space if the flow is measure-preserving. Thanks for pointing out my mistake! |
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Apr 6 |
awarded | Student |
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Apr 6 |
comment |
Having trouble understanding the concept of “mixing” in dynamical systems. I edited my question to match the above comment. |
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Apr 6 |
revised |
Having trouble understanding the concept of “mixing” in dynamical systems. deleted 34 characters in body |
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Apr 6 |
comment |
Having trouble understanding the concept of “mixing” in dynamical systems. As for the second part, I agree that I've put it in an unnecessarily confusing manner. The point is that in the infinite limit, $\phi^{t}(B)$ and $A$ are the same set of points, so their intersection is just going to be that set. So I should have said $\lim_{t \rightarrow \infty} \mu(\phi^{t}(B) \cap A) = \mu(A) = \mu(B)$. The rest of the argument follows. Does this work? |
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Apr 6 |
comment |
Having trouble understanding the concept of “mixing” in dynamical systems. $\lim_{t \rightarrow \infty} \phi^{t}(B)$ is the set of points to which $B$ evolves under the flow in the infinite time limit. |
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Apr 6 |
revised |
Having trouble understanding the concept of “mixing” in dynamical systems. edited tags |
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Apr 6 |
comment |
Having trouble understanding the concept of “mixing” in dynamical systems. It just occurred to me that maybe the problem is that for a mixing system my choice of $A$ does not correspond to a measurable set. Is this the case? If so, how do we square that with the fact that the dynamics is measure-preserving? |
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Apr 6 |
awarded | Editor |
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Apr 6 |
revised |
Having trouble understanding the concept of “mixing” in dynamical systems. added 38 characters in body |
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Apr 6 |
asked | Having trouble understanding the concept of “mixing” in dynamical systems. |
