7 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 the coupled nonlinear Schrödinger equations be the system given by … possess transverse super-homoclinic orbits. The conjecture asserts that the global stable and unstable inva…

Let $\gamma_3$ be the homoclinic family, let $\mathfrak{D}$ be the critical curve, and let $m_1,m_2,m_3$ be the mass parameters. Gamma-3 separation conjecture. The $\gamma_3$ famil…

Let $\gamma_2$ be the triple Copenhagen homoclinic family, let $\mathfrak{D}$ be the critical curve, and let $L_0$ and $L_2$ be the relevant libration points. Gamma-2 critical-curv…

Let $\gamma_1$ be the triple Copenhagen homoclinic family and let $\mathfrak{D}$ be the critical curve. Gamma-1 non-continuation conjecture. The $\gamma_1$ family never continues t…

Let $\gamma_{1,2,3}$ denote the short triple Copenhagen homoclinic orbits and let $\mathfrak{D}$ be the critical curve in parameter space. Belyakov-Devaney conjecture. Any paramete…

Let $A=(p^*,0)$, $B=(p_-,0)$, and $C=(p_-,s^*)$, where $s^*\approx 1.50815$. Consider the C-shaped homoclinic bifurcation curves in $(p,s)$-parameter space for the FitzHugh–Nagumo…