Abstract
We give the exact number of characteristic lines for homogeneous vector fields, when the number is finite. This in particular answers an open question posed by Llibre and Pilyugina (J Dynam Diff Equ 21:487–499, 2009).
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References
Griffiths P., Harris J.: Principles of Algebraic Geometry. Wiley Classics Library Edition, Wiley, New York (1994)
Llibre J., Pilyugina V.: Number of invariant straight lines for homogeneous polynomial vector fields of arbitrary degree and dimension. J. Dynam. Diff. Equ. 21, 487–499 (2009)
Perko L.: Differential Equations and Dynamical Systems, Texts in Applied Math. Vol. 7. 3rd edn. Springer, New York (2001)
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Rong, F. On The Number of Characteristic Lines for Homogeneous Vector Fields. J Dyn Diff Equat 24, 823–825 (2012). https://doi.org/10.1007/s10884-012-9259-0
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DOI: https://doi.org/10.1007/s10884-012-9259-0