4 ms·
Arnold's Cat (2018)
- deleted 2y ago[deleted]
- JadeNB 2y agoThe page doesn't say why matrices need to have whole-number (really just integer) entries, but I'd suspect it's because bad approximations to non-integer rationals accumulate sufficiently to make the recurrence unrecognizable.
- pepinator 2y agoIt says that the underlying action is on the torus (R/Z)^2. If the entries of the matrix are not integers, do we have a well defined action on the torus? It seems to me that the answer is no because Z^2 would not be invariant by the action.
- JadeNB 2y ago> It says that the underlying action is on the torus (R/Z)^2. If the entries of the matrix are not integers, do we have a well defined action on the torus? It seems to me that the answer is no because Z^2 would not be invariant by the action. Ah, good point.
- kkylin 2y agoOne can still define a map by taking the fractional part of the matrix-vector product, but the resulting map won't be continuous (with respect to the topology of the torus). In addition, if one wants the map be a homeomorphism (continuous with continuous inverse) then the determinant must have absolute value 1.
- TaurenHunter 2y agoI clicked the link wondering if it would be about this "Arnold the Cat" or perhaps related to Simon's Cat: https://www.publishersweekly.com/9780316638111 https://www.publishersweekly.com/9780316638111
- 01HNNWZ0MV43FF 2y agoCool, though I didn't understand it at all
- bnetd 2y ago[dead]