Concerning periodic points in mappings of continua

In this paper we present some conditions which are sufficient for a mapping to have periodic points. © 1988 American Mathematical Society

Jungck theorem for triangular maps and related results

[EN] We prove that a continuous triangular map G of the n-dimensional cube In has only fixed points and no other periodic points if and only if G has a common fixed point with every continuous triangular map F that is nontrivially compatible with G. This is an analog of Jungck theorem for maps of a real compact interval. We also discuss possible extensions of Jungck theorem, Jachymski theorem and some related results to more general spaces. In particular, the spaces with the fixed point property and the complete invariance property are considered.The firrt author was supported by the State Committee for Scienti c Research (Poland) Grant No. 2 PO3A 033 11 and the second author by the Slovak Grant Agency, Grant No. 1/4015/97.Grinc, M.; Snoha, L. (2000). Jungck theorem for triangular maps and related results. Applied General Topology. 1(1):83-92. https://doi.org/10.4995/agt.2000.3025SWORD83921

An Extension of Sharkovsky’s Theorem to Periodic Difference Equations

We present an extension of Sharkovsky’s Theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties