5 problems

Let $\mathfrak{D}$ and $\mathfrak{D}_3$ be the critical parameter curves, and let $v_c=(m_1,m_2,m_3)$ be their separating point. Critical-curve separation conjecture. The separatio…

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 $\hat{s}_{1,1}$ be the terminal parameter of the $\gamma_1$ homoclinic family along $\ell_1(s)$. Gamma-1 termination conjecture. … Numerical continuation gives the lower bound…

Let $\hat{s}_{2,k}$ denote the terminal parameter for the $\gamma_2$ homoclinic family along the parameter line $\ell_k(s)$, for $k=1,2,3$. Gamma-2 continuation conjecture. … The n…

Let $\hat{s}_{1,k}$ denote the terminal parameter for the continuation of the $\gamma_1$ family along the parameter line $\ell_k(s)$, for $k=1,2,3$. Numerical lower-bound conjectur…