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Limits of renormalizable polynomials

Hiroyuki Inou

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Recommended by L Bunimovich

We give a criterion for closedness of combinatorial properties in the parameter space of polynomials having connected Julia set and apply it to the renormalizability of polynomials. Consequently, we give two sufficient conditions for the limit of a convergent sequence of renormalizable polynomials to be again renormalizable.


PACS

02.10.De Algebraic structures and number theory

02.10.Ox Combinatorics; graph theory

MSC

37F10 Polynomials; rational maps; entire and meromorphic functions (See also 32A10, 32A20, 32H02, 32H04)

37F25 Renormalization

37F20 Combinatorics and topology

Subjects

Mathematical physics

Dates

Issue 8 (August 2006)

Received 11 August 2005, in final form 13 June 2006

Published 7 July 2006



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