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Class returning coordinates of iteration maps in a dynamical system

asked 2019-02-26 19:19:20 +0200

imnotarobot gravatar image

Hi, I'm using sage to study certain rational maps in $1$ dimensional projective space. Specifically I'd like to calculate coordinate maps of $n$-th iteration. I know that there are nth_iterate and nth_iterate_map classes but it seems that nth_iterate class only works on specific points and nth_iterate_map class returns the whole dynamical system, not the coordinate maps. For example, if we define

sage: P.<x,y>=ProjectiveSpace(QQ,1); f=DynamicalSystem([x^2,y^2],domain=P)


sage: f.nth_iterate(P[x,y],2)

gives an error that it is unable to convert x to an element of Algebraic Field, and

sage: f.nth_iterate_map(2)

gives a dynamical system as follows.

Dynamical System of Projective Space of dimension 1 over Algebraic Field Defn: Defined on coordinates by sending (x : y) to (x^4 : y^4)

What I want is a class, or any method, that returns coordinate maps, probably as a list of maps in $x$ and $y$, of $n$-th iteration. In the previous example, it should return a list $[x^4,y^4]$. Any help will be appreciated. Thanks in advance!

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answered 2019-02-27 19:54:31 +0200

rburing gravatar image

You can achieve this by

 sage: f.nth_iterate_map(2).defining_polynomials()
 (x^4, y^4)

As a general tip, if you have an object that you want to get information out of, try assigning it to a variable e.g.

f2 = f.nth_iterate_map(2)

and then type f2.<TAB>; this will suggest a list of methods.

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Asked: 2019-02-26 19:19:20 +0200

Seen: 285 times

Last updated: Feb 27 '19