Iterated Maps

Iterations or iterated maps or simply maps are the simplest way to describe non-linear systems.You can experiment with a map by using a calculator: you write a number and then hit repeatedly a function like cos. The trick is that ,starting from some initial value, you must compute the result and then feed this result again in the function. The set of numbers that you get from some starting value is called an orbit. You can write down a map with the formula x=f(x) where f(x) is an arbitrary expression. You can also have planar maps with two expressions:

   x = f(x,y)
   y = g(x,y)

A special case of planar maps are maps in the complex number plane. z = f(z) The famous Mandelbrot set is produced with a complex map.

Perhaps the simplest map that shows chaos is the logistic map: x = r*x(1-x)

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Maintained by Giuseppe Zito:Giuseppe.Zito@cern.ch: last update 17 Nov 97