4 problems

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Mating conjecture for the antipodally symmetric cubic map
Consider the degree- $3$ bicritical rational map commuting with the antipodal involution $\alpha(z)=-1/\overline z$ , shown in the source with parameters $X=-.235$ and $Y=.213$ , and…
Conjectureopencomplex-dynamics polynomial-matings rational-mapsarXiv posted 2 days ago
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The conjugate-or-complementary limb conjecture for cubic polynomial matings
Let $\mathcal{S}_1$ denote the space of cubic polynomials with a fixed critical point, and let $f,g\in\mathcal{S}_1$ be postcritically finite polynomials. Two polynomials are matea…
Conjectureopencomplex-dynamics cubic-polynomials polynomial-matingsarXiv posted 2 days ago
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Douady–Hubbard mateability conjecture for quadratic polynomials
Douady–Hubbard's conjecture. The points $c_1$ and $c_2$ do not lie in conjugate limbs of the Mandelbrot set if and only if
Conjectureopenmandelbrot-set polynomial-matings quadratic-dynamicsarXiv posted 2 days ago
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Tan Lei's mating-and-capture conjecture for cubic Newton maps
Tan Lei's conjecture. The set of all cubic Newton maps can be completely described in terms of matings and captures.
Conjectureopencomplex-dynamics newton-maps polynomial-matingsarXiv posted 2 days ago

Mating conjecture for the antipodally symmetric cubic map