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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)

##### 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
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