Name: On the accumulation points of non-periodic orbits of a difference equation of fourth order
Keywords: Difference equations, Boundedness, Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics, Differentiable dynamical systems, First integral, Classificació AMS::39 Difference and functional equations::39A Difference equations, Sistemes dinàmics diferenciables, Accumulation points, Kronecker's theorem

descriptionPublicationkeyboard_double_arrow_right Report 01 Jan 2023 English

Authors: Linero Bas, Antonio; Mañosa Fernández, Víctor; Nieves Roldán, Daniel;

handle: 2117/390919

On the accumulation points of non-periodic orbits of a difference equation of fourth order

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Abstract

In this paper, we are interested in analyzing the dynamics of the fourth-order difference equation x_{n+4}=max{x_{n+3},x_{n+2},x_{n+1},0}-x_n, with arbitrary real initial conditions. We fully determine the accumulation point sets of the non-periodic solutions that, in fact, are configured as proper compact intervals of the real line. This study complements the previous knowledge of the dynamics of the difference equation already achieved in [M. Csörnyei, M. Laczkovich, Monatsh. Math. 132 (2001), 215-236] and [A. Linero Bas, D. Nieves Roldán, J. Difference Equ. Appl. 27 (2021), no. 11, 1608-1645]

This work has been supported by the grant MTM2017-84079-P funded by MCIN/AEI/10.13039/501100011033 and by ERDF “A way of making Europe”, by the European Union. The second autor acknowledges the group research recognition 2021 SGR 01039 from Agència de Gestió d’Ajuts Universitaris i de Recerca

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Difference equations, Boundedness, Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics, Differentiable dynamical systems, First integral, Classificació AMS::39 Difference and functional equations::39A Difference equations, Sistemes dinàmics diferenciables, Accumulation points, Kronecker's theorem, Non-periodic solutions

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