As A Shift Operator
The baker's map can be understood as the two-sided shift operator on the symbolic dynamics of a one-dimensional lattice. Consider, for example, the bi-infinite string
where each position in the string may take one of the two binary values . The action of the shift operator on this string is
that is, each lattice position is shifted over by one to the left. The bi-infinite string may be represented by two real numbers as
and
In this representation, the shift operator has the form
which can be seen to be the inverse of the un-folded baker's map given above.
Read more about this topic: Baker's Map
Famous quotes containing the word shift:
“Youve just fulfilled the first role of law enforcement. Make sure when your shift is over you go home alive.”
—David Mamet, U.S. screenwriter, and Brian DePlama. Jimmy Malone (Sean Connery)