Dynamics of projective morphisms having identical canonical heights | Zendy

Kawaguchi Shu | Zendy; Silverman Joseph H. | Zendy

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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.

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