In mathematics, an interval exchange transformation is a kind of dynamical system that generalises the idea of a circle rotation. The phase space consists of the unit interval, and the transformation acts by cutting the interval into several subintervals, and then permuting these subintervals.
Read more about Interval Exchange Transformation: Formal Definition, Properties, Generalizations
Famous quotes containing the words interval and/or exchange:
“The yearning for an afterlife is the opposite of selfish: it is love and praise for the world that we are privileged, in this complex interval of light, to witness and experience.”
—John Updike (b. 1932)
“To coöperate in the highest as well as the lowest sense, means to get our living together. I heard it proposed lately that two young men should travel together over the world, the one without money, earning his means as he went, before the mast and behind the plow, the other carrying a bill of exchange in his pocket. It was easy to see that they could not long be companions or coöperate, since one would not operate at all. They would part at the first interesting crisis in their adventures.”
—Henry David Thoreau (1817–1862)