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- W1704671780 abstract "In this paper we give the bifurcation diagram of the family of cubic vector fields $dot z=z^3+ epsilon_1z+epsilon_0$ for $zin mathbb{C}mathbb{P}^1$, depending on the values of $epsilon_1,epsilon_0inmathbb{C}$. The bifurcation diagram is in $mathbb{R}^4$, but its conic structure allows describing it for parameter values in $mathbb{S}^3$. There are two open simply connected regions of structurally stable vector fields separated by surfaces corresponding to bifurcations of homoclinic connections between two separatrices of the pole at infinity. These branch from the codimension 2 curve of double singular points. We also explain the bifurcation of homoclinic connection in terms of the description of Douady and Sentenac of polynomial vector fields." @default.
- W1704671780 created "2016-06-24" @default.
- W1704671780 creator A5012415802 @default.
- W1704671780 date "2015-06-23" @default.
- W1704671780 modified "2023-09-27" @default.
- W1704671780 title "The bifurcation diagram of cubic polynomial vector fields on $mathbb{C}mathbb{P}^1$" @default.
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