JadeNB 3 days ago

The 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.

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  • pepinator 3 days 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.

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    • kkylin 3 days ago

      One 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.

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    • JadeNB 3 days 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.

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bnetd 3 days ago

Managed to time-sync the frame transitions to an old Juno Reactor album and i'm right back in some weird MTV esque vibe like I'm watching Beavis and Butthead or Duckman or something.

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