Re: cycles and chaos

You seem to be interested in Herman's rings and finite Blaschke
products in dynamics.
Most often you would study different kinds of Henon type dynamics
which are closely related to Siegel disks.
You have to differentiate between complex dynamics and the less symmetrical generalized Henon type 2d dynamics.
James Meiss has some good papers online about this area:
http://amath.colorado.edu/faculty/jdm/
http://amath.colorado.edu/faculty/jdm/research.html
H.R. Dullin and J. D. Meiss, "Generalized Hénon Maps: the Cubic Polynomial Diffeomorphisms of the Plane." Physica D 143(1-4): 265-292 (2000) .
maria pereira wrote:

I need to know if the function f(xt+1)=Ax t- xt(Bxt2 - C)/(D xt2 - C) can exhibit cyclical (repelling) and chaotic dynamics and, if it does, to what parameter values that occurs. What should I do? What readings do you advise me to pursue? 


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