6 problems

Let a fourth-order Hamiltonian system have two reversible symmetries, and suppose it undergoes a Belyakov-Devaney bifurcation. The Belyakov-Devaney bifurcation is the transition at…

Let a dynamical system be reversible with respect to an involution of type $(n,m)$, with $m\geq 1$ and $n\geq 2$, and let it have a symmetric Kronecker $n$-torus with a Diophantine…

Consider the two remaining codimension $1$ normal forms of planar reversible vector fields: the nodal type and the focal type. Nodal and focal conjecture. The nodal and focal norma…

Let $X_{\lambda}(x,y)$ be a fixed type of normal form for a one-parameter family of codimension $1$ reversible vector fields. Let $\lambda_1$ and $\lambda_2$ be two distinct real v…

A reversible system may have symmetric homoclinic and heteroclinic cycles undergoing codimension-1 bifurcations. The associated mixed dynamics is the coexistence of infinitely many…

Generic non-degeneracy conjecture. The required non-degeneracy holds for most $L-F$ systems under consideration.