Effectivity of dynatomic cycles for morphisms of projective varieties using deformation theory

Author:
Benjamin Hutz

Journal:
Proc. Amer. Math. Soc. **140** (2012), 3507-3514

MSC (2010):
Primary 37P35, 37P55

DOI:
https://doi.org/10.1090/S0002-9939-2012-11192-X

Published electronically:
February 22, 2012

MathSciNet review:
2929019

Full-text PDF

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Abstract: Given an endomorphism of a projective variety, by intersecting the graph and the diagonal varieties we can determine the set of periodic points. In an effort to determine the periodic points of a given minimal period, we follow a construction similar to cyclotomic polynomials. The resulting zero-cycle is called a dynatomic cycle, and the points in its support are called formal periodic points. This article gives a proof of the effectivity of dynatomic cycles for morphisms of projective varieties using methods from deformation theory.

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Additional Information

**Benjamin Hutz**

Affiliation:
The Graduate Center, The City University of New York, New York, New York 10016

Email:
bhutz@gc.cuny.edu

DOI:
https://doi.org/10.1090/S0002-9939-2012-11192-X

Keywords:
Periodic point,
dynatomic polynomial,
dynamical system

Received by editor(s):
November 29, 2010

Received by editor(s) in revised form:
March 14, 2011, and April 10, 2011

Published electronically:
February 22, 2012

Communicated by:
Matthew A. Papanikolas

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.