IJPAM: Volume 64, No. 1 (2010)

ON SHARKOVSKII'S THEOREM

Indranil Bhaumik$^1$, Binayak S. Choudhury$^2$
$^{1,2}$Department of Mathematics
Bengal Engineering and Science University
Shibpur, Howrah, 711103, West Bengal, INDIA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.Let $f$ be a continuous real valued function defined over the real line. If $f$ has a periodic point of least period $n$, the existence of any other periodic point of least period $m$ different from $n$ is completely discovered by Russian mathematician Alexander Nikolaevich Sharkovskii. In this paper we have proved Sharkovskii's Theorems in a very simple way. In the last section we have discussed some important consequences and generalization of these theorems.

Received: August 8, 2010

AMS Subject Classification: 37E05, 37D45, 37C25

Key Words and Phrases: Sharkovskii's Theorem, Sharkovskii ordering, fixed point, periodic point

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 1