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Asymptotic Dynamics of a Difference Equation with a Parabolic Equilibrium

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Abstract

The aim of this work is the study of the asymptotic dynamical behaviour, of solutions that approach parabolic fixed points in difference equations. In one dimensional difference equations, we present the asymptotic development for positive solutions tending to the fixed point. For higher dimensions, through the study of two families of difference equations in the two and three dimensional case, we take a look at the asymptotic dynamic behaviour. To show the existence of solutions we rely on the parametrization method.

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Acknowledgements

A. Gasull is partially supported by Spanish MCYT/FEDER Grant No. MTM2016-77278-P and Gov. Catalunya Grant No. 2017SGR 1617; B. Coll and R. Prohens are partially supported by Spanish and European Regional Development Funds (ERDF, FEDER) MICINN MTM2017-83568-P and MICINN MTM2014-54275-P grants. The authors want to thank prof. Rafael Ortega for his comments and suggestions during the realization of this work. We also would like to thank the anonymous referees for their careful reading of the paper and their constructive criticism.

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  1. Dept. de Matemàtiques i Informàtica, IAC3 Institute of Applied Computing and Community Code, Universitat de les Illes Balears, 07122, Palma de Mallorca, Illes Balears, Spain

    B. Coll & R. Prohens

  2. Dept. de Matemàtiques, Universitat Autònoma de Barcelona Edifici C, 08193, Bellaterra, Barcelona, Spain

    A. Gasull

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  1. B. Coll
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Coll, B., Gasull, A. & Prohens, R. Asymptotic Dynamics of a Difference Equation with a Parabolic Equilibrium. Qual. Theory Dyn. Syst. 19, 70 (2020). https://doi.org/10.1007/s12346-020-00406-0

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