7 problems

Fix $\jmath^*>1$ and use the center bundle equations described above. Higher-symmetry discrete-wave conjecture. Generically, there is a deleted neighbourhood…

Fix $\jmath^*\in\mathbb{N}$ and use the center bundle equations and hypotheses described above. Combined RSB and TSB epicycle conjecture. If $\jmath^*=1$, given a hyperbolic equili…

Fix $\jmath^*\in\mathbb{N}$ and let $(\varepsilon,\mu)\in\mathbb{R}^2$. Consider the center bundle equations … where $v\in\mathbb{C}$, $\omega_{\mathrm{rot}}\neq0$, the functions…

Let $n\in\mathbb{N}$, let $\lambda=(\lambda_1,\ldots,\lambda_n)\in\mathbb{R}^n$, and consider the center bundle equations displayed in the preceding conjecture, with smooth, unifor…

Let $\mathcal{B}^2$ be the unit disk equipped with Neumann boundary conditions, and let $\lambda>0$ be the diffusion parameter in the Ginzburg–Landau equation. For a positive integ…

Consider spiral waves in the cyclic-dominance reaction–diffusion system, and let the coexistence equilibrium point be the spatially homogeneous equilibrium with…

Convergence conjecture. The Taylor jet of the vector field on this manifold converges exponentially as $R$ increases, and the limiting equation is given by the skew-product equatio…