The rational rank of the support of generalized power series solutions of differential and $q$-difference equations

Autor:	Cano, J., Ayuso, P. Fortuny
Rok vydání:	2024
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Complex Variables Mathematics - Dynamical Systems 34M25 (Primary) 30D05 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Given a differential or $q$-difference equation $P$ of order $n$, we prove that the set of exponents of a generalized power series solution has its rational rank bounded by the rational rank of the support of $P$ plus $n$. We also prove that when the support of the solution has maximum rational rank, it is convergent. Using the Newton polygon technique, we show also that in the maximum rational rank case, an initial segment can always be completed to a true solution. The techniques are the same for the differential and the $q$-difference case. Comment: 21 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2406.06115 Zobrazit plný text záznamu View this record from Arxiv