Tune shift with amplitude of the system. When the tune reaches resonant values, it can be unstable, and thus a tune-shift with amplitude can limit the stability region, or dynamic aperture. In classical mechanics, a simple example of a system with tune shift with amplitude is a pendulum. In accelerator physics, both the transverse and the longitudinal dynamics show tune shift with amplitude. A simple model of the transverse dynamics is of an oscillator with a single sextupole, it is referred to as the Hénon map. Another model for this case is the Standard Map. An important example is the typical case of distributed
Kavli Institute for the Physics and Mathematics of the Universe Kavli Institute for the Physics and Mathematics of the Universe The Kavli Institute for the Physics and Mathematics of the Universe (IPMU) is an international research institute for physics and mathematics situated in Kashiwa, Japan, near Tokyo. Its full name is ""Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo Institutes for Advanced Study, the University of Tokyo, Kashiwa, Japan"". The main subjects of study at IPMU are particle physics, high energy physics, astrophysics, astronomy and mathematics. The institute addresses five key questions: "How did the universe begin? What is its fate? What is it