10/21/2007, 07:19 AM

describes the function your assumption produces, i.e.:

and so on, while still allowing and retaining the property .

By the term orbit I'm refering to a term from dynamical systems where, given a point x, the sequence {x, f(x), f(f(x)), ...} is referred to as the orbit of f from x which is a way of referring to iteration without referring to the t in . By using it this way, though, I'm slightly misusing it, since its a sequence, and not a function. Here I'm using it as a function , sorry if it was confusing. One of the reasons why I like the term 'orbit' so much is that it pairs nicely with iterate which, given t, is a function . I've discussed these terms here as well.

Andrew Robbins

and so on, while still allowing and retaining the property .

By the term orbit I'm refering to a term from dynamical systems where, given a point x, the sequence {x, f(x), f(f(x)), ...} is referred to as the orbit of f from x which is a way of referring to iteration without referring to the t in . By using it this way, though, I'm slightly misusing it, since its a sequence, and not a function. Here I'm using it as a function , sorry if it was confusing. One of the reasons why I like the term 'orbit' so much is that it pairs nicely with iterate which, given t, is a function . I've discussed these terms here as well.

Andrew Robbins