On the accumulation points of non-periodic orbits of a difference equation of fourth order
| Autor: | Linero Bas, Antonio, Mañosa Fernández, Víctor, Nieves Roldán, Daniel |
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| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. UPCDS - Grup de Sistemes Dinàmics de la UPC |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
Difference equations
Boundedness Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics [Àrees temàtiques de la UPC] 37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems [Classificació AMS] Differentiable dynamical systems First integral 39 Difference and functional equations::39A Difference equations [Classificació AMS] Sistemes dinàmics diferenciables Accumulation points Kronecker's theorem Non-periodic solutions |
| Popis: | Preprint 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 |
| Databáze: | OpenAIRE |
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