Abstract
Up to this point our primary focus has been on arithmetic dynamics of rational maps on ℙ1. In this chapter we take a look at dynamics in higher dimensions. Even over ℂ, although there is now a significant body of knowledge, it seems fair to say that complex dynamics on ℙN is still in its infancy. And arithmetic dynamics in higher dimensions is at present a patchwork of results from which a general theory is yet to emerge. Our goal in this chapter is to provide a glimpse into two aspects of this developing theory by highlighting two ways in which higher-dimensional dynamics differs significantly from the one-dimensional case.
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© 2007 Springer Science+Business Media, LLC
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Silverman, J.H. (2007). Dynamics in Dimension Greater Than One. In: The Arithmetic of Dynamical Systems. Graduate Texts in Mathematics, vol 241. Springer, New York, NY. https://doi.org/10.1007/978-0-387-69904-2_8
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DOI: https://doi.org/10.1007/978-0-387-69904-2_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-69903-5
Online ISBN: 978-0-387-69904-2
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