Timeline for Entropy conjecture for flows
Current License: CC BY-SA 2.5
12 events
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| Dec 22, 2015 at 21:59 | comment | added | John B | An old one, but I am still a bit confused. Why don't you consider simply the time 1-map? | |
| Sep 24, 2010 at 22:42 | comment | added | rpotrie | Interesting! It seems something to think about. Why not post it as an answer? Since the question is vague, it is natural that answers are too. | |
| Sep 24, 2010 at 20:02 | comment | added | Andrey Gogolev | version (growth in time and the size of the "small set" versus growth in homology) maybe useful and guarantee positive entropy. I understand that this is very vague. | |
| Sep 24, 2010 at 20:01 | comment | added | Andrey Gogolev | It seems like you would like to ignore flow on simple manifolds like spheres. Just a wild idea: take a cycle, flow it for some time. Then perturb the cycle (cut and reglue, but on a small set, not touching the cycle outside the small set). The result is new cycle. If there is some grouth then we say that we see some topological growth. Say, your homology is Z^2, you start with (0,1) and end up with (2,10). As it is, it's not going to work for sure (think of horocycle flow in negative curvature), but a some quantitative | |
| Sep 24, 2010 at 19:47 | comment | added | Andrey Gogolev | this restriction on comment length is no good | |
| Sep 24, 2010 at 8:48 | history | edited | rpotrie | CC BY-SA 2.5 |
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| Sep 24, 2010 at 8:47 | comment | added | rpotrie | BTW, thanks for the first reference, I didn't know it. I will include it in the question as reference. | |
| Sep 23, 2010 at 21:16 | history | edited | rpotrie | CC BY-SA 2.5 |
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| Sep 23, 2010 at 21:10 | comment | added | rpotrie | The previous "question" would be if there is an analogue of the entropy conjecture for flows. Markov properties sound more local to me, essentially, I would prefer some global conditions (similar to the spectral radius of the action of homology, for flows with global sections it is clear how to define this, but what about other flows, for example for geodesic flows). | |
| Sep 23, 2010 at 20:25 | comment | added | Andrey Gogolev | This is really vague. Which "previous question" are you referring to? The only thing that comes to mind is that if you have a global section then you are in business, if not maybe it makes sense to take several sections and ask for some sort of markov property (the weaker the better). Some readily available references on entropy conjecture 1) math.psu.edu/katok_a/pub/ConjectureAboutEntropy1986.pdf 2) math.toronto.edu/shub/SHUB-ICM2006.pdf | |
| Sep 23, 2010 at 20:09 | history | edited | rpotrie | CC BY-SA 2.5 |
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| Sep 23, 2010 at 19:52 | history | asked | rpotrie | CC BY-SA 2.5 |