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Dynamics of projective morphisms having identical canonical heights
Author(s) -
Kawaguchi Shu,
Silverman Joseph H.
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm022
Subject(s) - mathematics , morphism , projective test , degree (music) , pure mathematics , polynomial , dynamics (music) , julia set , combinatorics , mathematical analysis , physics , acoustics
Let ϕ , ψ :ℙ N → ℙ N be morphisms of degree at least 2 whose canonical heights ĥ ϕ and ĥ ψ are identical. We draw various conclusions about the Green functions, Julia sets, and canonical local heights of ϕ and ψ . We use this information to completely characterize ϕ and ψ in the following cases: (i) ϕ and ψ are polynomial maps in one variable; (ii) ϕ is the d th‐power map; (iii) ϕ is a Lattès map.