A Characterization of Multiplicity-Preserving Global Bifurcations of Complex Polynomial Vector Fields

Álvarez, M., Gasull, A., Prohens, R.: Topological classification of polynomial complex differential equations with all the critical points of center type. J. Differ. Equ. Appl. 16(5), 411–423 (2010)

Andronov, A.A., Leontovich, E.A., Gordon, I.I., Maier, A.G.: Qualitative Theory of Second-Order Dynamic Systems. Wiley, New York (1973). (Original: Nakua, Moscow 1967)

Artés, J.C., Llibre, J., Schlomiuk, D.: The geometry of quadratic differential systems with a weak focus of second order. Int. J. Bifurc. Chaos 16(11), 3127–3194 (2006)

Benzinger, H.E.: Plane autonomous systems with rational vector fields. Trans. Am. Math. Soc. 326(2), 465–483 (1991)

Benzinger, H.E.: Julia sets and differential equations. Proc. Am. Math. Soc. 117(4), 939–946 (1993)

Branner, B., Dias, K.: Classification of polynomial vector fields in one complex variable. J. Differ. Equ. Appl. 16(5), 463–517 (2010)

Brickman, L., Thomas, E.S.: Conformal equivalence of analytic flows. J. Differ. Equ. 25, 310–324 (1977)

Buff, X., Chéritat, A.: Ensembles de julia quadratiques de mesure de lebesgue strictement positive. C. R. Acad. Sci. Paris 341(11), 669–674 (2005)

Buff, X., Tan, L.: Dynamical convergence and polynomial vector fields. J. Differ. Geom. 77(1), 1–41 (2007)

Christopher, C., Rousseau, C.: The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point. Int. Math. Res. Not. 9, 2494–2558 (2014)

Dias, K.: Enumerating combinatorial classes of complex polynomial vector fields in $$\mathbb{C}$$. Ergod. Theory Dyn. Syst. 33, 416–440 (2013)

Dias, K., Tan, L.: On parameter space of complex polynomial vector fields in $$\mathbb{C}$$. J. Differ. Equ. 260, 628–652 (2016)

Douady, A., Estrada, F., Sentenac, P.: Champs de vecteurs polynomiaux sur $$\mathbb{C}$$. Unpublished manuscript

Fathi, A., Laudenbach, F., Poenaru, V.: Traveaux de thurston sur les surfaces. Asterisque, pp. 66–67 (1979)

Gardiner, F.P., Hu, J.: Finite earthquakes and the associahedron. In: Teichmüller theory and moduli problems, pp. 179–194 (2010)

Garijo, A., Gasull, A., Jarque, X.: Normal forms for singularities of one dimentional holomorphic vector fields. Electron. J. Differ. Equ. 2004(122), 1–7 (2004)

Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, New York (1983)

Hájek, O.: Notes on meromorphic dynamical systems, I. Czech. Math. J. 16(1), 14–27 (1966)

Hájek, O.: Notes on meromorphic dynamical systems, II. Czech. Math. J. 16(1), 28–35 (1966)

Hájek, O.: Notes on meromorphic dynamical systems, III. Czech. Math. J. 16(1), 36–40 (1966)

Jenkins, J.: Univalent Functions. Springer, Berlin (1958)

Llibre, J., Schlomiuk, D.: The geometry of quadratic differential systems with a weak focus of third order. Can. J. Math. 56(2), 310–343 (2004)

Mardešić, P., Roussarie, R., Rousseau, C.: Modulus of analytic classification for unfoldings of generic parabolic diffeomorphisms. Mosc. Math. J. 4, 455–498 (2004)

Muciño-Raymundo, J., Valero-Valdés, C.: Bifurcations of meromorphic vector fields on the Riemann sphere. Ergod. Theory Dyn. Syst. 15(6), 1211–1222 (1995)

Needham, D., King, A.: On meromorphic complex differential equations. Dyn. Stab. Syst. 9, 99–121 (1994)

Neumann, D.: Classification of continuous flows on 2-manifolds. Proc. Am. Math. Soc. 48(1), 73–81 (1975)

Oudkerk, R.: The parabolic implosion for $$f\_0(z)=z+z^{\nu +1}+o(z^{\nu +2})$$. Ph.D. thesis, University of Warwick (1999)

Rousseau, C.: Analytic moduli for unfoldings of germs of generic analytic diffeomorphims with a codimension $$k$$ parabolic point. Ergod. Theory Dyn. Syst. 35, 274–292 (2015)

Rousseau, C., Teyssier, L.: Analytical moduli for unfoldings of saddle-node vector fields. Mosc. Math. J. 8(3), 547–614 (2008)

Shishikura, M.: Bifurcation of parabolic fixed points. In: Lei, T. (ed.) The Mandelbrot Set, Theme and Variations. Cambridge University Press, Cambridge (2000)

Sverdlove, R.: Vector fields defined by complex functions. J. Differ. Equ. 34, 427–439 (1979)