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

Fuente: arXiv
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Main Authors: Bas, Antonio Linero, Mañosa, Víctor, Roldán, Daniel Nieves
Format: Preprint
Published: 2023
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_version_ 1866910823194034176
author Bas, Antonio Linero
Mañosa, Víctor
Roldán, Daniel Nieves
author_facet Bas, Antonio Linero
Mañosa, Víctor
Roldán, Daniel Nieves
contents 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].
format Preprint
id arxiv_https___arxiv_org_abs_2306_12061
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle On the accumulation points of non-periodic orbits of a difference equation of fourth order
Bas, Antonio Linero
Mañosa, Víctor
Roldán, Daniel Nieves
Dynamical Systems
39A10, 39A23, 39A05, 37E99
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].
title On the accumulation points of non-periodic orbits of a difference equation of fourth order
topic Dynamical Systems
39A10, 39A23, 39A05, 37E99
url https://arxiv.org/abs/2306.12061