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

In this paper, we are interested in analyzing the dynamics of the fourth-order difference equation xn+4 =max{xn+3, xn+2, xn+1, 0} -xn, 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 Csörnyei and Laczkovich (2001) [5] and Linero Bas and Nieves Roldán (2021) [10].
"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 author acknowledges the group research recognition 2021 SGR 01039 from Agència de Gestió d'Ajuts Universitaris i de Recerca"
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