Timeline for Packing measure and Kleinian groups
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 23, 2015 at 21:48 | vote | accept | John B | ||
| Dec 27, 2015 at 21:01 | |||||
| Dec 22, 2015 at 11:31 | comment | added | Pablo Shmerkin | For dynamical objects Hausdorff and packing dimensions often (though not always) agree. Although I don't like the definition of fractal as the equality of Hausdorff and packing dimension, this equality does say something about the geometry of the object - very roughly, that its size is the same at all small scales. So I would say that throughout dynamics packing dimension occurs naturally! | |
| Dec 21, 2015 at 21:57 | vote | accept | John B | ||
| Dec 23, 2015 at 21:46 | |||||
| Dec 21, 2015 at 21:57 | comment | added | John B | Thank you very much for your reply. I knew the two first works. But let me insist on the "dynamical systems" aspect, thus reformulating a bit: Are there any other "natural" occurrences of packing dimension and/or packing "measure" in the context of dynamical systems? I tend to disagree with you that having positive packing measure is a good argument; even the Patterson-Sullivan procedure goes precisely by avoiding this problem, somehow in a blunt manner, but quite to the point, and so I also don't like my own example of Kleinian groups. By the way, I'm quite fond of your work. | |
| Dec 21, 2015 at 21:25 | history | answered | Pablo Shmerkin | CC BY-SA 3.0 |