Some results on periodic orbits of functions
DOI:
https://doi.org/10.14393/BEJOM-v6-2025-76862Keywords:
Periodic points, periodic orbits, Intermediate Value Theorem, Li-Yorke TheoremAbstract
In this work we will study several concepts related to real continuous functions in one variable, highlighting results related to fixed points, periodic orbits and the Li-Yorke Theorem. This last theorem establishes that if a real function applies the interval [a,b] to itself and has a point of period three, then it will have periodic points of any positive integer period. The results will be obtained mainly through applications of the Intermediate Value Theorem and Brouwer Fixed Point Theorem, two classic results in Mathematics, whose formulation and geometric interpretations are relatively simple and whose applications are quite relevant in several sciences.
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Copyright (c) 2025 Mayara Beatriz Ferreira Drumond , Wenderson Marques Ferreira, Eder Marinho Martins
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