Geodesic
The Sharkovskii theorem as a tool for increasing the level of combinatorial thinking
The Teaching of Mathematics, XXVIII (2025) no. 1, p. 1

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The Sharkovskii theorem is an important mathematical result of the last century, which significantly helped the development of a modern mathematical field -- chaos theory. The Sharkovskii theorem is related to an interval on the real axis and a single-valued function. However, it was later generalized in various ways. This article will focus on the multivalued generalization of the Sharkovskii theorem, which has also found application in the theory of differential equations. We will show that the considered multivalued generalization of the Sharkovskii theorem is also suitable in mathematics education, especially for increasing the level of combinatorial thinking. We present some examples for pupils of different levels.
DOI : 10.57016/TM-RJEF8495
Classification : 97F60, 97K20, F64, K24
Keywords: Sharkovskii theorem, combinatorial thinking, chaos theory, concept of function, graph reading, numeracy. 
Karel Pastor; Radka Dofková. The Sharkovskii theorem as a tool for increasing the level of combinatorial thinking. The Teaching of Mathematics, XXVIII (2025) no. 1, p. 1 . doi: 10.57016/TM-RJEF8495
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