7 problems

Consider the Rössler system … is exactly … An available approach is to establish that the saddle-focus equilibrium $E_0$ possesses a homoclinic trajectory. The conjecture concerns…

Let $P$ be the parameter space of the Rössler system, let $p\in P$ be a trefoil parameter, and let $K(v)\in\{1,2\}^{\mathbf{N}}$ be the sequence obtained by recording whether the s…

Heteroclinic-knot complexity conjecture. The more $\Lambda$ is knotted with itself, the more knot types occur in the template $T_p$; in particular, every knot type on $T_p$, save p…

Termination conjecture. For every periodic trajectory $T\in C$, there exists a parameter $v\in P$ such that, as the Rössler system is perturbed from $p$ to $v$ through parameter sp…

Generalized trefoil-parameter conjecture. There exists a neighborhood $O\subseteq P$ of $p$ such that, for every $v\in O$, there is a smooth vector field $G_v$, hyperbolic on its n…

Let $P$ be the parameter space, let $p\in P$ be a heteroclinic parameter generating a heteroclinic knot $K$, and let $F_p$ be the corresponding vector field. Assume the conditions…

Let $P$ be the parameter space, let $p\in P$ be the trefoil parameter, and let $F_v$ denote the vector field corresponding to $v\in P$. Let $L(0,1)$ be the template associated with…