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Could somebody please give a big picture description of what exactly is the object of study in the area of Algebraic Dynamics? Is it related to Dynamical Systems? If yes in what sense? Also, what is the main mathematical discipline underpinning Algebraic Dynamics? Is it algebraic geometry, differential geometry e.t.c.?


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up vote 2 down vote accepted

The Wiki article states that it is a combination of dynamical systems and number theory. I know it's a redirect, but WP's information on this point is probably reliable enough :)

(Are you checking here because you are not comfortable with WP info? It is a serious question which I'm curious about.)

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So you are saying that arithmetic dynamics is the same as algebraic dynamics? – Manos Aug 27 '12 at 18:03
What is WP info? – Manos Aug 27 '12 at 18:04
@manos WP=Wikipedia. Yes, I arrived at this page by searching for "Algebraic dynamics", and that page redirected to arithmetic dynamics. Usually it's OK to assume the validity of such redirects. – rschwieb Aug 27 '12 at 18:12
I am pretty comfortable with Wikipedia. – Manos Aug 27 '12 at 18:47
It may also refer to rational map actions (quotient of polynomials) on algebraic varieties, or dynamics given by differential equations where the vector fields are polynomial (this last one relates closely to Hilbert's 16th problem). – William Dec 24 '12 at 11:38

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