Timeline for Can a zero entropy automorphism of the torus have a Li-Yorke pair?
Current License: CC BY-SA 3.0
9 events
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| May 27, 2017 at 2:21 | history | edited | Andres Koropecki | CC BY-SA 3.0 |
added 99 characters in body
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| S May 27, 2017 at 0:58 | history | edited | Andres Koropecki | CC BY-SA 3.0 |
Fixed mistake at the end of the proof (T fibers over the circle but it doesn't have to induce an automorphism on each fiber)
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| S May 27, 2017 at 0:58 | history | suggested | CommunityBot | CC BY-SA 3.0 |
Fixed mistake at the end of the proof (T fibers over the circle but it doesn't have to induce an automorphism on each fiber)
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| May 27, 2017 at 0:55 | review | Suggested edits | |||
| S May 27, 2017 at 0:58 | |||||
| Aug 30, 2016 at 19:29 | comment | added | Andres Koropecki | Yes, if you consider just homeomorphisms, you can have all sorts of weird things. For example a transitive homeomorphism with a fixed point would be an example with a Li-Yorke pair, and this can have zero entropy (for example it can be the time-one map of a flow, as the example described in this thread) | |
| Aug 30, 2016 at 13:46 | comment | added | Will Brian | Oh, I see. I'm looking at the torus as a topological space, and as such it has lots of "automorphisms" (which I took to mean self-homeomorphisms). You're looking at it as a Lie Group, where all the "automorphisms" are translations by a group element (linear). Looking at the question again, I think your reading might be the intended one, and your answer now makes sense to me. (Interestingly, I think one gets the opposite answer under my reading of the question.) | |
| Aug 30, 2016 at 0:11 | comment | added | Andres Koropecki | I thought linear automorphisms are all there is. Am I missing something? | |
| Aug 29, 2016 at 18:21 | comment | added | Will Brian | I'm a bit confused when you say that your claim answers the question negatively. Your claim suggests that the question might have a negative answer, but it leaves open the possibility that a non-linear automorphism of the torus might have zero entropy and have a Li-Yorke pair. Correct? | |
| Aug 29, 2016 at 17:41 | history | answered | Andres Koropecki | CC BY-SA 3.0 |