Abstract and Applied Analysis

Stability of Rotation Pairs of Cycles for the Interval Maps

Taixiang Sun, Hongjian Xi, Hailan Liang, Qiuli He, and Xiaofeng Peng

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Abstract

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

Article information

Source
Abstr. Appl. Anal., Volume 2011 (2011), Article ID 931484, 9 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313171121

Digital Object Identifier
doi:10.1155/2011/931484

Mathematical Reviews number (MathSciNet)
MR2773643

Zentralblatt MATH identifier
1209.33017

Citation

Sun, Taixiang; Xi, Hongjian; Liang, Hailan; He, Qiuli; Peng, Xiaofeng. Stability of Rotation Pairs of Cycles for the Interval Maps. Abstr. Appl. Anal. 2011 (2011), Article ID 931484, 9 pages. doi:10.1155/2011/931484. https://projecteuclid.org/euclid.aaa/1313171121


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References

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