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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
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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.