O'Reilly logo

Dynamics in One Complex Variable. (AM-160), 3rd Edition by John Milnor

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Appendix C. Rotations, Continued Fractions, and Rational Approximation

(Compare §§11 and 15.) The study of recurrence is a central topic in many parts of dynamics: How often and how closely does an orbit return to a neighborhood of its initial point? In the case of irrational rotations of a circle we can give a rather precise description of the answer. This description, which has its roots in classical number theory, turns out to be important not only in holomorphic dynamics, but also in celestial mechanics and other areas where “small divisor” problems occur.

image

Figure 46. Successive orbit points under a rotation through the angle of ξ = –2 =.2360… ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required