Over-Rotation Pairs (pr + 1, (pr + 1)m + r) for Periodic Orbits of Unimodal Expanding Self-Maps on the Interval

Caihong Han, Taixiang Sun, Hongjin Xi and Guangwang Su

Journal of Mathematics, 2026, vol. 2026, 1-9

Abstract: Let m≥3,r≥2 and p be positive integers. Write Px,m=xm−2xm−1+1/xm−1x−1 and Fm,p,rx=xpm+2xpm−xmxr−1pm+1−1+xxpm−1xpm+1−1Px,m+xpm+2xm−1xrpm+1−1Px,m+1. In this paper, we prove that if f is an unimodal expanding self-map on the interval with an expanding constant λ satisfying Fm,p,rλ≥0, then f has a periodic orbit with the over-rotation pair pr+1,pr+1m+r. In addition, this paper also points out that when Fm,p,rλ 1 but no periodic orbit with an over-rotation pair pr+1,pr+1m+r.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2026/1678945.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2026/1678945.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1678945

DOI: 10.1155/jom/1678945

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().