10 problems

The alpha-limit conjecture for generic real polynomial maps
arXiv@arxiv
Alpha-limit conjecture. There is some non-empty open subset $A\subset f(\mathbb{R}\mathrm{P}^2)$ such that $\alpha_{N_f}(x)$ is equal to the set of non-regular points of the bounda…
Conjectureopendynamical-systems julia-sets newton-maps
0
Shishikura's Julia-set connectivity conjecture for Newton maps of entire functions
arXiv@arxiv
Shishikura's connectivity conjecture. The Julia set of every Newton map of an entire function is connected.
Conjectureopencomplex-dynamics julia-sets newton-maps
2
Extension of the entropy continuity theorem for postcritically-finite Newton maps
arXiv@arxiv
Let $f$ be a postcritically-finite Newton map of degree $d$ . The entropy function $h:{\mathcal N}_d^{\rm pf}\to\mathbb R$ is upper semi-continuous at $f$ . If $f$ is non-renormaliza…
Conjectureopendynamical-systems entropy newton-maps
0
Simple-dynamics conjectures for Newton maps of real polynomial maps
arXiv@arxiv
Simple-dynamics conjectures. The following properties hold:
Conjectureopendynamical-systems julia-sets newton-maps
1
Weak plainness conjecture for real Newton maps on the plane
arXiv@arxiv
Weak plainness conjecture. Then:
Conjectureopenjulia-sets newton-maps real-dynamics
0
Barna-type plainness conjecture for real Newton maps
arXiv@arxiv
Plainness conjecture. Every $p$ satisfying the hypotheses of Barna's theorem is a plain map.
Conjectureopennewton-maps real-dynamics
0
Tan Lei's component conjecture for cubic Newton maps with prescribed Head's angles
arXiv@arxiv
Tan Lei's component conjecture. Given any component $(\beta,\alpha)$ of $(0,1/2)\setminus\Xi$ , there is a unique connected component of
Conjectureopencomplex-dynamics newton-maps parameter-spaces
0
Tan Lei's irrational Head's angle realization conjecture for cubic Newton maps
arXiv@arxiv
Tan Lei's irrational realization conjecture. Each irrational angle $\theta\in\Xi$ can also be realized as the Head's angle of some cubic Newton map.
Conjectureopencomplex-dynamics newton-maps realization-problems
0
Tan Lei's parameter-space conjecture for the cubic Newton family
arXiv@arxiv
Tan Lei's parameter-space conjecture. The fundamental part of the cubic Newton family is homeomorphic to the quotient of the union of those two subsets by the equivalence relation…
Conjectureopencomplex-dynamics newton-maps parameter-spaces
1
Tan Lei's mating-and-capture conjecture for cubic Newton maps
arXiv@arxiv
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-matings
0