periodic point

Let f:XX be a functionMathworldPlanetmath and fn its n-th iteration. A point x is called a periodic pointMathworldPlanetmath of period n of f if it is a fixed point of fn. The least n for which x is a fixed point of fn is called prime period or least period.

If f is a function to or to then a periodic point x of prime period n is called hyperbolic if |(fn)(x)|1, attractive if |(fn)(x)|<1 and repelling if |(fn)(x)|>1.

Title periodic point
Canonical name PeriodicPoint
Date of creation 2013-03-22 12:43:38
Last modified on 2013-03-22 12:43:38
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 14
Author mathwizard (128)
Entry type Definition
Classification msc 26A18
Defines hyperbolic periodic point
Defines attractive periodic point
Defines repelling periodic point
Defines least period
Defines prime period