On the Sharkovsky’s property of Darboux functions

Ryszard J. Pawlak

doi:10.2478/v10127-009-0010-0

.blurhash-client-img { display: none !important; }

On the Sharkovsky’s property of Darboux functions

Tatra Mountains Mathematical Publications

Volume 42 (2009): Issue 1 (April 2009)

By: Ryszard J. Pawlak

Open Access

|Nov 2012

Abstract

Examinations of Sharkovsky’s property for discontinuous functions are usually connected with complex considerations. In this paper we ascertain the relation between two families of functions giving possibility to resolve the question about Sharkovsky’s property of functions belonging to one of those families into examination J1 property of the second of them.

References

[1] ALSED`A, L.-LLIBRE, J.-MISIUREWICZ, M.: Combinatorial Dynamics and Entropy in Dimension One. Adv. Ser. Nonlinear Dynam., Vol. 5, World Scientific, Singapore, 1993.10.1142/1980
Search in Google Scholar
[2] BLOCK, L. S.-COPPEL, W. A.: Dynamics in One Dimension. Lecture Notes in Math., Vol. 1513, Springer-Verlag, Berlin, 1992.
Search in Google Scholar
[3] BRUCKNER, A. M.: Differentiation of Real Functions. CRM Monogr. Ser., Vol. 5, AMS, Providence, RI, 1994.10.1090/crmm/005
Search in Google Scholar
[4] BRUCKNER, A. M.-CEDER, J. G.: Darboux continuity, Jahresber. Deutsch. Math.-Verein. 67 (1965), 93-117.
Search in Google Scholar
[5] ENGELKING, R.: General Topology. Monografie Matematyczne, Vol. 60, PWN-Polish Scientific Publishers, Warszawa, 1977.
Search in Google Scholar
[6] KELLUM, K. L.: Iterates of almost continuous functions and Sharkovskii’s theorem, Real Anal. Exchange 14 (1989), 420-422.10.2307/44151956
Search in Google Scholar
[7] SZUCA, P.: Punkty Sta_le Odwzorowa´n Typu Darboux. Doctoral Thesis, Gda´nsk, 2003. (In Polish)
Search in Google Scholar
[8] SZUCA, P.: Sharkovski˘ı’s theorem holds for some discontinuous functions, Fund. Math. 179 (2003), 27-41.10.4064/fm179-1-3
Search in Google Scholar