zbMATH — the first resource for mathematics

Coexistence of cycles of a continuous map of the line into itself. (English) Zbl 0890.58012
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 \(n_1\).
Reviewer: Reviewer (Berlin)

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
Full Text: DOI