Timeline for Maximal Hausdorff dimension of the set on which derivatives do not agree
Current License: CC BY-SA 4.0
17 events
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| S May 22 at 21:39 | history | bounty ended | Nate River | ||
| S May 22 at 21:39 | history | notice removed | Nate River | ||
| May 20 at 12:49 | vote | accept | Nate River | ||
| May 20 at 12:38 | answer | added | an_ordinary_mathematician | timeline score: 8 | |
| May 20 at 9:37 | history | edited | Nate River | CC BY-SA 4.0 |
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| May 20 at 9:28 | history | edited | Nate River | CC BY-SA 4.0 |
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| May 20 at 9:01 | history | edited | Nate River | CC BY-SA 4.0 |
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| S May 20 at 9:01 | history | bounty started | Nate River | ||
| S May 20 at 9:01 | history | notice added | Nate River | Draw attention | |
| Apr 25, 2021 at 13:46 | comment | added | Dave L Renfro | @Keo Moos: Unless I'm overlooking something, what you suggest seems fine. In fact, I believe I made a similar comment about something similar (achieving maximal Hausdorff dimension for a single graph by gluing appropriate graphs) in a comment somewhere, probably MSE, within the last 2 or 3 years. | |
| Apr 24, 2021 at 20:00 | comment | added | Leo Moos | @DaveLRenfro If you can get any dimension less than one, can't you stitch these functions together to some $h: \mathbf{R} \to \mathbf{R}$ and reparametrise it via a diffeomorphism $(0,1) \to \mathbf{R}$? This would give dimension one, no? | |
| Apr 24, 2021 at 19:48 | comment | added | Dave L Renfro | Unfortunately, I don't know what possibilities exist for the Hausdorff dimension of sets belonging to Zahorski's $M_4$ class. Probably any dimension strictly less than $1$ is possible, but I don't know about achieving dimension $1.$ | |
| Apr 24, 2021 at 19:48 | comment | added | Dave L Renfro | Using $h = f - g,$ the question becomes: If $h'$ exists a.e. and $h' = 0$ a.e., then what is supremum of the Hausdorff dimension of the set at which $h'$ exists and differs from zero? (Several versions, actually, depending on whether none or one or both of the $h'$ exists requirements include infinite derivatives.) Off-hand I don't know (probably $1$ even for the strongest version and with "a.e." replaced with "everywhere"), but my answer to Set of zeroes of the derivative of a pathological function may be of use. (continued) | |
| Apr 24, 2021 at 15:47 | comment | added | LSpice | Is there an obvious reason that the 'supremal' dimension should be achieved? | |
| Apr 24, 2021 at 15:18 | answer | added | Johan Aspegren | timeline score: -1 | |
| Apr 12, 2021 at 7:08 | answer | added | mlk | timeline score: 4 | |
| Apr 12, 2021 at 0:47 | history | asked | Nate River | CC BY-SA 4.0 |