Interval Exchange Transformation - Formal Definition

Formal Definition

Let and let be a permutation on . Consider a vector

of positive real numbers (the widths of the subintervals), satisfying

Define a map

called the interval exchange transformation associated to the pair as follows. For

let

and let

Then for, define

T_{\pi,\lambda}(x) = x - a_i + a'_i

if lies in the subinterval . Thus acts on each subinterval of the form by an orientation-preserving isometry, and it rearranges these subintervals so that the subinterval at position is moved to position .

Read more about this topic:  Interval Exchange Transformation

Famous quotes containing the words formal and/or definition:

    “Two clergymen disputing whether ordination would be valid without the imposition of both hands, the more formal one said, “Do you think the Holy Dove could fly down with only one wing?””
    —Horace Walpole (1717–1797)

    “No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
    —Florence Nightingale (1820–1910)