Abstract.
In this paper using theory of linear operators and normal forms we generalize a result of Poincaré [11] about the non-existence of local first integrals for systems of differential equations in a neighbourhood of a singular point. As an application of the generalized result, and under more weak conditions we obtain a result of Furta [8] about local first integrals of semi-quasi-homogeneous systems. Moreover, for diffeomorphisms and periodic differential systems we give definitions of their first integrals, and generalize the previous results about systems of differential equations to diffeomorphisms in a neighbourhood of a fixed point and to periodic differential systems in a neighbourhood of a constant solution.
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Received: September 29, 2000; revised: March 13, 2001
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Li, W., Llibre, J. & Zhang, X. Local first integrals of differential systems and diffeomorphisms. Z. angew. Math. Phys. 54, 235–255 (2003). https://doi.org/10.1007/s000330300003
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DOI: https://doi.org/10.1007/s000330300003