Simple recursions displaying interesting evolutions

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arxiv 2405.00370 v1 pith:NBHB7QJJ submitted 2024-05-01 nlin.SI

Francesco Calogero This is my paper · ORCID

classification nlin.SI

keywords recursionssimpleascertainedbehaviourcompletelydisplayingevolutionsidentified

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Some simple nonlinear recursions which can be completely managed are identified and the behaviour of all their solutions is ascertained.

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Some properties of the simple nonlinear recursion $y(\ell + 1) = [1-y(\ell)]^p$ with $p$ an arbitrary positive integer
nlin.SI 2025-01 conditional novelty 4.0 of 10

For the recursion y_{n+1}=(1-y_n)^p with p a positive integer, real solutions are either asymptotically 2-periodic between 0 and 1 or diverge, depending on the initial value.