11 problems

For each $n\geq 3$, consider the family $r_{n,a}$ in the $a$-plane and the parameters $a_k$ associated with the potential centers of hyperbolic components, where $k$ is odd and…

Let $q<0.5$, let $S^q$ be the stability domain of the fixed points of the fractional-order Mandelbrot set (FOM), and let the main body of the associated fractal set be understood i…

Let $q\in(0,1)$, let $S^q$ denote the stability domain for the fixed points of the fractional-order Mandelbrot set (FOM), and let the main body of the underlying fractional-order M…

Let $n\geq3$. The multicomplex Mandelbrot set ${\mathcal{M}_{n}}$ is considered through its principal and idempotent $n$-dimensional slices, including slices associated with regula…

The tricomplex Mandelbrot set has principal 3D slices, including one regular octahedron and another polyhedral slice. Regular tetrahedron conjecture. The latter slice is a regular…

Multi-Mandelbrot connectedness conjecture. The set ${\cal MM}$ is a connected set in $\mathbb{C}^4$.

Star-shaped connectedness conjecture. The set of infinitely well-behaved pairs $(0,c_1)$ is star-shaped connected.

Let ${\mathcal{M}^p}$ be the generalized Mandelbrot set for the polynomial $Q_{p,c}(z)=z^p+c$, where $z,c\in\mathbb{C}$ and $p\geq 2$ is an integer. The real-slice conjecture. If…

Consider a template Mandelbrot set associated with a template exhibiting less regularity than a regular template, and let its boundary be the boundary of that set. Boundary-dimensi…

Let ${\bf s} \in {\cal L}(\{0,1\})$ be a symbolic template, and let $(c_0,c_1) \in \mathbb{C}^2$. The fixed-template Mandelbrot set is … and the fixed-map Mandelbrot set is … Here…

Let $Q_{p,c}(z)=z^p+c$ with $z,c\brin\mathbb{C}$ and integer $p\geq 2$, and let $\mathcal{M}^p$ be the generalized Mandelbrot set for this polynomial. Real-intersection conjecture.…