29ef4a024ef51f5d085d469a289a16b8 aimmat_a2024v9n1p73-88.pdf b1ea7c2487481dc34f7682cada8039583e83a502 aimmat_a2024v9n1p73-88.pdf f4dc578028e1a412ef7d6dcda71052ae83425856c87675654a247758d3e59ace aimmat_a2024v9n1p73-88.pdf Title: Time-reversibility and integrability of $p:-q$ resonant vector fields Subject: We study the local analytical integrability in a neighborhood of $p:-q$ resonant singular point of a two-dimensional vector field and its connection to time-reversibility with respect to the non-smooth involution $ \varphi(x,y)=(y^{p/q},x^{q/p}). $ Some generalizations of the theory developed by Sibirsky for the $1:-1$ resonant case to the $p:-q$ resonant case are presented. Keywords: planar systems of ODEs; time-reversibility; integrability; resonant singularity Author: Jaume Gine1 Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Tue Nov 28 02:40:58 2023 CET ModDate: Tue Nov 28 02:43:09 2023 CET Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 16 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 271567 bytes Optimized: no PDF version: 1.5 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- RMXOIA+NimbusRomNo9L-Regu Type 1 Custom yes yes no 29 0 KHSNVN+rtxr Type 1 Builtin yes yes no 30 0 CQNNVH+NimbusRomNo9L-MediItal Type 1 Custom yes yes no 32 0 YDDWJW+NimbusRomNo9L-Medi Type 1 Custom yes yes no 33 0 HGKVCD+NimbusRomNo9L-ReguItal Type 1 Custom yes yes no 34 0 LJGOMS+txsy Type 1 Builtin yes yes no 35 0 ELIYRQ+rtxmi Type 1 Builtin yes yes no 36 0 ESZOCS+txsyb Type 1 Builtin yes yes no 38 0 YPNPDT+txex Type 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