Rational Periodic Points for Degree Two Polynomial Morphisms on Projective Space

Details Rational Periodic Points for Degree Two Polynomial Morphisms on Projective Space Rational Periodic Points for Degree Two Polynomial Morphisms on Projective Space

2008-11-19

arxiv.org/abs/0811.3225v2

Mathematics

Dynamical Systems

to appear in Acta Arithmetica

Scientific paper

This article addresses the existence of $\Q$-rational periodic points for morphisms of projective space. In particular, we construct an infinitely family of morphisms on $\P^N$ where each component is a degree 2 homogeneous form in $N+1$ variables which has a $\Q$-periodic point of primitive period $\frac{(N+1)(N+2)}{2} + \lfloor \frac{N-1}{2}\rfloor$. This result is then used to show that for $N$ large enough there exists morphisms of $\P^N$ with $\Q$-rational periodic points with primitive period larger that $c(k)N^k$ for any $k$ and some constant $c(k)$.

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