JadeNB 3 days ago | next |

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.

pepinator 3 days ago | root | parent |

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.

kkylin 3 days ago | root | parent | next |

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.

JadeNB 3 days ago | root | parent | prev |

> 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.

bnetd 3 days ago | prev | next |

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.