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On the asymptotic behaviour of difference equations: piecewise-linear analysis
  • Andres Garcia,
  • Andrés García
Andres Garcia

Corresponding Author:[email protected]

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Andrés García
Grupo de Investigacion en Multifísica Aplicada (GIMAP), Universidad Tecnológica Nacional-FRBB


In this paper, general one-dimensional difference equations (DE) are studied. In fact, the asymptotic behaviour of such DE's will be studied via an algebraic closed-form condition plus a linear DE. Some examples are presented including the Collatz sequence, proving the existence of at most one invariant set surrounding the number 1: {1, 2, 4}. Some conclusions will be also depicted.