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Weak hyperbolicity on periodic orbits for polynomials

โœ Scribed by J. Rivera-Letelier

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
74 KB
Volume
334
Category
Article
ISSN
1631-073X

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โœฆ Synopsis

We prove that if the multipliers of the repelling periodic orbits of a complex polynomial grow at least like n 5+ฮต with the period, for some ฮต > 0, then the Julia set of the polynomial is locally connected when it is connected. As a consequence for a polynomial the presence of a Cremer cycle implies the presence of a sequence of repelling periodic orbits with "small" multipliers. Somewhat surprisingly the proof is based on measure theorical considerations.

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