7 problems

Consider the extended directed graph formed from the equilibrium $\mathbf{0}$, the primary periodic orbits $\Gamma_{*}$ and $\Gamma_{1}^{\pm}$, infinitely many additional periodic…

Let $a$ be the parameter in the border-collision normal form, and consider the saddle chaotic set associated with the period-five heteroclinic cycle at $a\approx 0.9592$. Its unsta…

Let the boundary of the continuum of Bianchi type $\mathrm{VIII}$ periodic orbits be obtained in the limit $N_1N_2N_3\to 0$. A type $\mathrm{II}$ heteroclinic chain of period four…

Consider a general $(N,m)$-graph with maximally-active fixed points, meaning fixed points with the largest number of active nodes. When $N=p \mod (m+1)$ with $p\neq 0,1$, all maxim…

The paper studies heteroclinic cycles in rings of coupled oscillators, whose invariant subspaces can produce robust attracting dynamics and non-ergodic behaviour. Typicality conjec…

Let $f$ be a dynamical system with an attracting heteroclinic cycle between more than two hyperbolic periodic solutions, in the more general setting suggested by the paper. Invaria…

Let $\varepsilon_{31}^*$ and $\varepsilon_{30}^*$ be the parameter values delimiting the interval in which the pair of non-conservative period-3 saddles exists, and suppose their J…