Stability of Rotation Pairs of Cycles for the Interval Maps

Let C0(I) be the set of all continuous self-maps of the closed interval I, and P(u,v)={f∈C0(I):f has a cycle with rotation pair (u,v)} for any positive integer v>u. In this paper, we prove that if (2mns,2mnt)⊣(γ,λ), then P(2mns,2mnt)⊂  int  P(γ,λ), where m≥0 is integer, n≥1 odd, 1≤s...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2011-01, Vol.2011 (2011), p.4078-4086
Main Authors: Sun, Taixiang, Xi, Hongjian, Liang, Hailan, He, Qiuli, Peng, Xiaofeng
Format: Article
Language:English
Subjects:
Functions, Continuous
Mappings (Mathematics)
Mathematics
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Summary:Let C0(I) be the set of all continuous self-maps of the closed interval I, and P(u,v)={f∈C0(I):f has a cycle with rotation pair (u,v)} for any positive integer v>u. In this paper, we prove that if (2mns,2mnt)⊣(γ,λ), then P(2mns,2mnt)⊂  int  P(γ,λ), where m≥0 is integer, n≥1 odd, 1≤s
ISSN:1085-3375
1687-0409
DOI:10.1155/2011/931484