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Theory Lunch
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Institute of Cybernetics, Tallinn
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Theory Lunch | Institute of Cybernetics, Tallinn Skip to primary content Skip to secondary content Theory Lunch Institute of Cybernetics, Tallinn Search Main menu Home Previous lunches About Post navigation ← Older posts A Remarkable Property of Real-Valued Functions on Intervals of the Real Line Posted on October 17, 2019 by Silvio Capobianco Reply Today the 17 October 2019 I discussed a very remarkable fixed point theorem discovered by the Ukrainian mathematician Oleksandr Micholayovych Sharkovsky . We recall that a periodic point of period for a function is a point such that . With this definition, a periodic point of period is also periodic of period for every which is a multiple of . If but for every from 1 to , we say that is the least period of . Theorem 1. (Sharkovsky’s “little” theorem) Let be an interval and let be a continuous function su. If has a point of least period 3, then it has points ...
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