I've written some experimental patches see 
(http://wiki.sagemath.org/dynamics/ArithmeticAndComplex) on moving 
functionality for dynamics on projective spaces into sage.

When I finished I had a thought that I'd like to gather some comments on 
from more experienced sage developers.

I've implemented most of the functionality in 
../schemes/generic/morphism.py:
class SchemeMorphism_polynomial_projective_space
class SchemeMorphism_point_projective_space

In hindsight, I'm not sure that was correct as that means the functionality 
will be inherited to subschemes (i.e morphisms/points of general projective 
varieties). Some of it could be modified to take subschemes into account, 
or simple checking could be performed in appropriate functions returning 
*NotImplemented* for subschemes.  On the other hand, I could create a new 
class just for endomorphisms/points of projective space.

a couple examples are:
- a function to return the dynatomic polynomial
- a function to check if the rational map is a morphism
- determining the complete cyclegraph over finite fields
- several others on rational preperiodic points and heights

Comments?

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