Academic Journal
On the accumulation points of non-periodic orbits of a difference equation of fourth order
| Title: | On the accumulation points of non-periodic orbits of a difference equation of fourth order |
|---|---|
| Authors: | Linero Bas, Antonio, Mañosa Fernández, Víctor, Nieves Roldán, Daniel |
| Contributors: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. UPCDS - Grup de Sistemes Dinàmics de la UPC |
| Source: | Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Publication Status: | Preprint |
| Publisher Information: | Elsevier BV, 2024. |
| Publication Year: | 2024 |
| Subject Terms: | Difference equations, Boundedness, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics, Kronecker's Theorem, Classificació AMS::39 Difference and functional equations::39A Difference equations, Dynamical Systems (math.DS), Sistemes dinàmics diferenciables, 01 natural sciences, Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems, 39A10, 39A23, 39A05, 37E99, 0103 physical sciences, FOS: Mathematics, Differentiable dynamical systems, First integral, Mathematics - Dynamical Systems, 0101 mathematics, Accumulation points, Non-periodic solutions, Kronecker's theorem |
| Description: | 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]. |
| Document Type: | Article |
| File Description: | application/pdf |
| Language: | English |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2023.127895 |
| DOI: | 10.48550/arxiv.2306.12061 |
| Access URL: | http://arxiv.org/abs/2306.12061 https://ddd.uab.cat/record/299748 https://hdl.handle.net/2117/399256 https://doi.org/10.1016/j.jmaa.2023.127895 |
| Rights: | Elsevier TDM CC BY CC BY NC ND |
| Accession Number: | edsair.doi.dedup.....e0500b83c5f9ac6cbbcfc1172fc92974 |
| Database: | OpenAIRE |
| ISSN: | 0022247X |
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| DOI: | 10.1016/j.jmaa.2023.127895 |