Time-reversibility and integrability of p:-q resonant vector fields

arXiv2211.12411MaRDI QIDQ6418145

Joan Torregrosa, Jaume Giné, Valery G. Romanovski

Publication date: 22 November 2022

Abstract: We study 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 K.~S.~Sibirsky for $1:-1$ resonant case to the $p:-q$ resonant case are presented.

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