Rational Periodic Points for Degree Two Polynomial Morphisms on Projective Space

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 $c(k)$.

• Publication year

  2008

• Venue

  arXiv: Dynamical Systems

• Publication date

  2008-11-19

• Fields of study

  Mathematics

• Identifiers
  DOI 10.4064/AA141-3-3arXiv 0811.3225
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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