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:

    “Then the justice,
    In fair round belly with good capon lined,
    With eyes severe and beard of formal cut,
    Full of wise saws and modern instances;
    And so he plays his part.”
    —William Shakespeare (1564–1616)

    “The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
    —William James (1842–1910)