Dynatomic cycles for morphisms of projective varieties

TL;DR

This paper proves the effectiveness of dynatomic cycles for morphisms on projective varieties, analyzes their degrees and multiplicities, and explores the existence of periodic points with arbitrarily large primitive periods.

Contribution

It establishes the effectivity of dynatomic cycles and provides new insights into their degrees and multiplicities, advancing understanding of periodic points in algebraic dynamics.

Findings

Dynatomic cycles are effective for morphisms of projective varieties.

Degrees and multiplicities of these cycles are explicitly analyzed.

Existence of periodic points with arbitrarily large primitive periods is demonstrated.

Abstract

We prove the effectivity of the dynatomic cycles for morphisms of projective varieties. We then analyze the degrees of the dynatomic cycles and multiplicities of formal periodic points and apply these results to the existence of periodic points with arbitrarily large primitive periods.