5 problems

Let $O$ be the collection of vector fields under consideration, let $\mathcal{L}$ be the collection of Lorenz maps that form factor maps for vector fields $V\in O$, and let…

Let $\mathcal{R}$ be the collection of all maps $\mathcal{F}:[0,1]\to[0,1]$ that serve as factor maps for first-return maps $\psi_v:R\setminus W\to R$ of the Lorenz attractor, not…

Let $P$ be the parameter space, let $R_0$ and $R_1$ be the two components of the cross-section $R$, and let $h_v:R_0\cup R_1\to\mathbb{R}^2$ be the map specified in Fig. S. For…

Let $l_{A=0}$ be the curve forming the right boundary of the region $LA$, and let $O$ be the equilibrium of the Lorenz system. A homoclinic loop to $O$ is a trajectory leaving $O$…

Let $T$ be the Poincaré map on the cross-section $\Pi:\{z=r-1\}$, with discontinuity line $\Pi_0$ dividing $\Pi$ into $\Pi_+$ and $\Pi_-$. Let $M_-$ and $M_+$ be the points where t…