First-Return Limiting Notions and Rings of Sharkovsky Functions

First-Return Limiting Notions and Rings of Sharkovsky Functions

Helena Pawlak and Ryszard J. Pawlak

Source: Real Anal. Exchange Volume 34, Number 2 (2008), 549-564.

Abstract

In this paper we apply some elements of real analysis theory to the distinguishing of the certain subclass of the class of functions possessing Sharkovsky property. The main aim of this is connected with the answer to the following question: what kind of assumption should we impose on Sharkovsky function $f$ in order to have that there exists a ring of functions possessing Sharkovsky property containing $f$?

First Page: Show

Primary Subjects: 26A18, 37E15

Secondary Subjects: 26A15, 54C40, 54H25

Keywords: od-set; Darboux function; first-return continuity; $\cal S$-function; Sharkovsky function; ring of functions; trajectory; property $\cal J$; family substituted by a subfamily

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.rae/1256835205
Zentralblatt MATH identifier: 05652554
Mathematical Reviews number (MathSciNet): MR2569205

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