Timeline for Julia sets using other fields
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 10, 2012 at 15:21 | answer | added | Jörg Neunhäuserer | timeline score: 1 | |
| Nov 16, 2011 at 15:03 | answer | added | Tom Leinster | timeline score: 3 | |
| Nov 16, 2011 at 14:30 | history | edited | Joe Silverman |
added ds tag
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| Nov 16, 2011 at 14:29 | answer | added | Joe Silverman | timeline score: 16 | |
| Nov 16, 2011 at 13:41 | comment | added | Gerald Edgar | More promising, perhaps, would be fields $\mathbb C_p$. Complete metric, algebraically closed, but NOT locally compact. Why not start by studying the maps $z^2+c$ which were so interesting in $\mathbb C$... | |
| Nov 16, 2011 at 11:57 | comment | added | Jose Capco | I mean, I think, its easy to restrict the julia set to the real algebraic numbers and arrive to some non-compact set. But why would it be interesting to look at Julia sets this way? | |
| Nov 16, 2011 at 10:35 | comment | added | Fabian | Indeed. I guess I got carried away by the reductions mod p. | |
| Nov 16, 2011 at 10:22 | comment | added | Felipe Voloch | @Fabian I don't think Silverman's book does any local field of characteristic p. He certainly does the p-adics, but these have characteristic zero. They are also locally compact, so closed and bounded is compact there too. But, yes, sometimes Julia sets are empty and other things change. | |
| Nov 16, 2011 at 10:19 | comment | added | Fabian | Silverman's book "The Arithmetic of Dynamical Systems" deals with fields of characteristic p. In that situation there are maps with empty Julia sets and various other properties that differ from the situation over the complex numbers. | |
| Nov 16, 2011 at 9:38 | history | asked | Jose Capco | CC BY-SA 3.0 |