A simple approach to identify systems of nonlinear recursions featuring solutions whose evolution is explicitly ascertainable and which may be asymptotically isochronous as functions of the independent variable (a ticking time)

Francesco Calogero

A simple approach to identify systems of nonlinear recursions featuring solutions whose evolution is explicitly ascertainable and which may be asymptotically isochronous as functions of the independent variable (a ticking time)

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arxiv 2410.14448 v1 pith:FKHPH2QT submitted 2024-10-18 nlin.SI

Francesco Calogero This is my paper · ORCID

classification nlin.SI

keywords asymptoticallyfunctionsidentifyindependentisochronousnonlinearrecursionssolutions

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In this paper a procedure is described which allows to identify new systems of nonlinear recursions whose solutions are controllable and which may be asymptotically isochronous as functions of the independent variable (considered a ticking time).

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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.

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