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.?
What is exactly "Algebraic Dynamics"?
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$\begingroup$
abstract-algebra
arithmetic-dynamics
2 Answers
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From nLab:
In algebraic dynamics one typically studies discrete dynamical systems on algebraic varieties. Such a system is given by a regular endomorphism $D: X \to X$ of a variety $X$.
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The case over number fields is also called arithmetic dynamics...
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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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1@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. – 2012-08-27
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0I am pretty comfortable with Wikipedia. – 2012-08-27
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0It 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). – 2012-12-24