Abstract
Here we investigate the Minkowski box dimension of complex integral curves of the vector fields near resonant saddles in \({\mathbb {C}}^2\). The results provide the geometrical explanation of the order of the saddle points and a quantitative description for the non-integrability via monodromy.
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Acknowledgements
The work is supported by NSF of China (No. 11571072) and partially supported by NSF of China (No. 11871041).
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Wu, H., Xu, S. The Geometrical Demonstration of the Order of Resonant Saddle Points in \({\mathbb {C}}^2\). Qual. Theory Dyn. Syst. 19, 27 (2020). https://doi.org/10.1007/s12346-020-00370-9
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DOI: https://doi.org/10.1007/s12346-020-00370-9