Sharkovskij, A. N. Coexistence of cycles of a continuous map of the line into itself. (English) Zbl 0890.58012 Int. J. Bifurcation Chaos Appl. Sci. Eng. 5, No. 5, 1263-1273 (1995). Summary: Translation of the author’s famous article [Ukr. Mat. Zh. 16, No. 1, 61-71 (1964; Zbl 0122.17504)].The basic result of this investigation may be formulated as follows. Consider the set of natural numbers in which the following relationship is introduced: \(n_1\) precedes \(n_2\) \((n_1 \preceq n_2)\) if for any continuous mapping of the real line into itself the existence of a cycle of order \(n_2\) follows from the existence of a cycle of order \(n_1\). Cited in 2 ReviewsCited in 50 Documents MSC: 37E99 Low-dimensional dynamical systems 58-03 History of global analysis 39B12 Iteration theory, iterative and composite equations 01A75 Collected or selected works; reprintings or translations of classics 06A05 Total orders Citations:Zbl 0122.17504 PDFBibTeX XMLCite \textit{A. N. Sharkovskij}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 5, No. 5, 1263--1273 (1995; Zbl 0890.58012) Full Text: DOI