Acknowledgement
The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1C1C2011737). The second author was supported by research fund of Chungnam National University.
References
- I. Bendixson, Sur les courbes definies par des equations differentielles, Acta Math. 24 (1901), no. 1, 1-88. https://doi.org/10.1007/BF02403068
- J. Choy, Geometry of Uhlenbeck partial compactification of orthogonal instanton spaces and the K-theoretic Nekrasov partition functions, Adv. Math. 330 (2018), 763-809. https://doi.org/10.1016/j.aim.2018.03.037
- J. Choy and H.-Y. Chu, Polycycle omega-limit sets of flows on the compact Riemann surfaces and Eulerian path, arXiv:1609.08505.
- J. Choy and H.-Y. Chu, Dynamics of Riemannian 1-foliations on 3-manifolds, Taiwanese J. Math. 23 (2019), no. 1, 145-157. https://doi.org/10.11650/tjm/180605
- J. G. Espin Buendia and V. Jimenez Lopez, Some remarks on the ω-limit sets for plane, sphere and projective plane analytic flows, Qual. Theory Dyn. Syst. 16 (2017), no. 2, 293-298. https://doi.org/10.1007/s12346-016-0192-1
- K. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996), no. 3, 513-519. https://doi.org/10.1016/0370-2693(96)01088-X
- V. Jimenez Lopez and J. Llibre, A topological characterization of the ω-limit sets for analytic flows on the plane, the sphere and the projective plane, Adv. Math. 216 (2007), no. 2, 677-710. https://doi.org/10.1016/j.aim.2007.06.007
- V. Jimenez Lopez and D. Peralta-Salas, Global attractors of analytic plane flows, Ergodic Theory Dynam. Systems 29 (2009), no. 3, 967-981. https://doi.org/10.1017/S0143385708000552
- S. K. Lando and A. K. Zvonkin, Graphs on surfaces and their applications, Encyclopaedia of Mathematical Sciences, 141, Springer-Verlag, Berlin, 2004. https://doi.org/10.1007/978-3-540-38361-1
- B. Mohar and C. Thomassen, Graphs on surfaces, Johns Hopkins Studies in the Mathematical Sciences, Johns Hopkins University Press, Baltimore, MD, 2001.
- A. Okounkov, Lectures on K-theoretic computations in enumerative geometry, in Geometry of moduli spaces and representation theory, 251-380, IAS/Park City Math. Ser., 24, Amer. Math. Soc., Providence, RI, 2017. https://doi.org/10.1090/pcms/024