The multipliers of periodic points in one-dimensional dynamics

Marco Martens; Welington De Melo

doi:10.1088/0951-7715/12/2/003

The multipliers of periodic points in one-dimensional dynamics

Marco Martens
, Welington De Melo

Mathematics

Instituto National de Matemática Pura e Aplicada

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

It will be shown that the smooth conjugacy class of an S-unimodal map which has neither a periodic attractor nor a Cantor attractor is determined by the multipliers of the periodic orbits. This generalizes a result by M Shub and D Sullivan (1985 Expanding endomorphism of the circle revisited Erg. Theor. Dyn. Sys. 5 285-9) for smooth expanding maps of the circle.

Original language	English
Pages (from-to)	217-227
Number of pages	11
Journal	Nonlinearity
Volume	12
Issue number	2
DOIs	https://doi.org/10.1088/0951-7715/12/2/003
State	Published - Mar 1999

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title = "The multipliers of periodic points in one-dimensional dynamics",

abstract = "It will be shown that the smooth conjugacy class of an S-unimodal map which has neither a periodic attractor nor a Cantor attractor is determined by the multipliers of the periodic orbits. This generalizes a result by M Shub and D Sullivan (1985 Expanding endomorphism of the circle revisited Erg. Theor. Dyn. Sys. 5 285-9) for smooth expanding maps of the circle.",

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AB - It will be shown that the smooth conjugacy class of an S-unimodal map which has neither a periodic attractor nor a Cantor attractor is determined by the multipliers of the periodic orbits. This generalizes a result by M Shub and D Sullivan (1985 Expanding endomorphism of the circle revisited Erg. Theor. Dyn. Sys. 5 285-9) for smooth expanding maps of the circle.

UR - https://www.scopus.com/pages/publications/0033100641

U2 - 10.1088/0951-7715/12/2/003

DO - 10.1088/0951-7715/12/2/003

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VL - 12

SP - 217

EP - 227

JO - Nonlinearity

JF - Nonlinearity

IS - 2

ER -

The multipliers of periodic points in one-dimensional dynamics

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