Kowalevskaya exponents and normal forms of planar dynamical systems. Application to integrability problem

Algaba Durán, AntonioGarcía García, Cristóbal, MatemáticoReyes Columé, ManuelGiné Mesa, Jaume2025-04-092025-04-092024Algaba, A., García, C., Reyes, M., & Giné, J. (2024). Kowalevskaya exponents and normal forms of planar dynamical systems. Application to integrability problem. In Communications in Contemporary Mathematics. World Scientific Pub Co Pte Ltd. https://doi.org/10.1142/s021919972550009917936683https://hdl.handle.net/10272/25355In this work dynamical properties of the solutions of differential systems in the plane are provided using certain constants related with the Kowalevskaya exponents. An orbital normal form that allows to study the existence of analytic and non-analytic first integrals is given. We apply the results to study the algebraic and analytic integrability around several singularities.engAtribución-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nd/3.0/es/Kowalevskaya exponents and normal forms of planar dynamical systems. Application to integrability problemjournal article10.1142/s0219199725500099open access12 Matemáticas