Montejano, L.; Shchepin, E. V. On periodic homeomorphisms of spheres. (English) Zbl 1016.57019 Algebr. Geom. Topol. 1, 435-444 (2001). The authors give natural lower estimates for metric data of orbits of a \(p\)-periodic homeomorphism \(h\) acting on the unit sphere \(S^n\) in the Euclidean \((n+1)\)-space. These are the shift \(\|h\|=\sup_{x\in S^n}\|h(x)- x\|\) and the maximal diameter \(\theta(h)\) of \(h\)-orbits. The bounds occurring herein are the following: \(\rho_p\) is the length of the side of a regular \(p\)-gon inscribed in the unit circle \(S^1\), \(d_p\) is the diameter of this \(p\)-gon, \(t_n\) is the edge length of the regular \((n+1)\)-simplex inscribed in \(S^n\). Reviewer: Emil Molnár (Budapest) MSC: 57S25 Groups acting on specific manifolds 52A40 Inequalities and extremum problems involving convexity in convex geometry 57N15 Topology of the Euclidean \(n\)-space, \(n\)-manifolds (\(4 \leq n \leq \infty\)) (MSC2010) Keywords:\(p\)-periodic homeomorphism; shift; maximal diameter PDFBibTeX XMLCite \textit{L. Montejano} and \textit{E. V. Shchepin}, Algebr. Geom. Topol. 1, 435--444 (2001; Zbl 1016.57019) Full Text: DOI arXiv EuDML EMIS References: [1] L Danzer, B Grünbaum, V Klee, Helly’s theorem and its relatives, Amer. Math. Soc. (1963) 101 · Zbl 0132.17401 [2] W Hurewicz, Über Abblindungen von endlichdimensionalen Räumen auf Teilmengen Cartesischer Räume, Sitrungsber. Preuss. Acad. Wiss. 34 (1933) 754 · Zbl 0008.13303 [3] D Montgomery, L Zippin, Topological transformation groups, Interscience Publishers, New York-London (1955) · Zbl 0068.01904 [4] M H A Newman, A theorem on periodic transformations of spaces, Quart. J. Math. 2 (1931) 1 · Zbl 0001.22703 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.