Timeline for Conjugating the Lyness 5-cycle into a rotation of the plane
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2012 at 3:45 | vote | accept | James Propp | ||
| Nov 2, 2012 at 3:45 | vote | accept | James Propp | ||
| Nov 2, 2012 at 3:45 | |||||
| Nov 2, 2012 at 1:27 | comment | added | James Propp | @Francois: That answers my question. Thanks! | |
| Nov 2, 2012 at 1:25 | vote | accept | James Propp | ||
| Nov 2, 2012 at 3:45 | |||||
| Oct 30, 2012 at 11:41 | comment | added | François Brunault | @James : Let $f : (x,y) \mapsto (y,\frac{y+1}{x})$ and $g : (x,y) \mapsto (1-y,1-\frac{y}{x})$. Then $g=hfh^{-1}$ with $h(x,y)=(-x,y+1)$. I didn't check this, but I knew the result had to be true since both maps are related to the functional equation of the dilogarithm :) By the way, the first versions of Beauville's article on arxiv use this functional equation to prove the result. | |
| Oct 29, 2012 at 16:33 | comment | added | James Propp | The reference is definitely helpful, especially the explicit formulas on page 3. However, I don't know how to explicitly see the map $(x:y:z) \mapsto (x(z-y):z(x-y):xz)$ (the birational transformation that Beauville and Blanc treat) as being conjugate to the map $(x:y:z) \mapsto (xy:(y+z)z:xz)$ (the projective version of the Lyness 5-cycle map). | |
| Oct 27, 2012 at 17:51 | history | answered | François Brunault | CC BY-SA 3.0 |