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Linear recurrences in the degree sequences of monomial mappings

Published online by Cambridge University Press:  01 October 2008

ERIC BEDFORD
Affiliation:
Indiana University, Bloomington, IN 47405, USA (email: bedford@indiana.edu)
KYOUNGHEE KIM
Affiliation:
Florida State University, Tallahassee, FL 32306, USA (email: kim@math.fsu.edu)

Abstract

Let A be an integer matrix, and let fA be the associated monomial map. We give a connection between the eigenvalues of A and the existence of a linear recurrence relation in the sequence of degrees.

Type
Research Article
Copyright
Copyright © 2008 Cambridge University Press

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References

[1]Bedford, E. and Kim, K. H.. On the degree growth of birational mappings in higher dimension. J. Geom. Anal. 14 (2004), 567596.CrossRefGoogle Scholar
[2]Diller, J. and Favre, C.. Dynamics of bimeromorphic maps of surfaces. Amer. J. Math. 123 (2001), 11351169.CrossRefGoogle Scholar
[3]Favre, C.. Les applications monomiales en deux dimensions. Michigan Math. J. 51 (2003), 467475.CrossRefGoogle Scholar
[4]Favre, C. and Jonsson, M.. Dynamical compactifications of ℂ2, arXiv: 0711.2770v1.Google Scholar
[5]Fornæss, J.-E. and Sibony, N.. Complex dynamics in higher dimension, II. Modern Methods in Complex Analysis (Princeton, NJ, 1992) (Annals of Mathematical Studies, 137). Princeton University Press, Princeton, NJ, 1995, pp. 135182.Google Scholar
[6]Hasselblatt, B. and Propp, J.. Degree-growth of monomial maps. Ergod. Th. & Dynam. Sys. 27(5) (2007), 13751397.CrossRefGoogle Scholar
[7]Russakovskii, A. and Shiffman, B.. Value distribution for sequences of rational mappings and complex dynamics. Indiana Univ. Math. J. 46 (1997), 897932.CrossRefGoogle Scholar
[8]Stanley, R. P.. Enumerative Combinatorics. Vol. 1. Wadsworth and Brooks/Cole, Monterey, CA, 1986.CrossRefGoogle Scholar