periodic point
Let f:X→X be a function and fn its n-th iteration. A point x is called a periodic point
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 ℝ to ℝ or ℂ to ℂ 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 |
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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 |