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- W2034852061 abstract "Abstract Self-maps everywhere defined on the projective space P N over a global field are the basic objects of study in the arithmetic of dynamical systems. In this paper we study the natural self-maps defined the following way: F is a homogeneous polynomial of degree d in ( N + 1 ) variables X i defining a smooth hypersurface. Suppose the characteristic of the field does not divide d and define the map of partial derivatives ϕ F = ( F X 0 , … , F X N ) . One can also compose such a map with an element of PGL N + 1 . In the case N = 1 , the smoothness condition means that F has only simple zeroes and we prove that a self-map of P 1 has constant multipliers if and only if it has the form ϕ ( X , Y ) = ( F Y , − F X ) . We recover in this manner classical dynamical systems like the Newton method for finding roots of polynomials or the Lattes map corresponding to the multiplication by 2 on an elliptic curve and the multiplication by n on the multiplicative group." @default.
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- W2034852061 date "2014-03-01" @default.
- W2034852061 modified "2023-10-17" @default.
- W2034852061 title "Almost Newton, sometimes Lattès" @default.
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- W2034852061 doi "https://doi.org/10.1016/j.jnt.2013.10.004" @default.
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