9 problems

Consider a non-gradient fast-slow system of higher dimension with a saddle on an unstable branch of the critical manifold. Let the instanton be the minimizer of the Freidlin–Wentze…

Let $W_{\textrm{loc}}^{\textup{c}}(0)$ be the local center manifold from Theorem … can be combined with the results on regular fold points to describe certain properties of the geo…

Fanning-out conjecture. This choice of family number 6 would still result in a fanning-out behavior similar to that established for the original system.

Codimension-one bifurcation conjecture. The codimension-one bifurcations of critical sets $\mathcal{C}[g]$ are characterised by the stated classification: precisely one set…

Persistence conjecture. For one fast and two slow variables, the critical set $\mathcal{C}[g]$ is persistent under perturbations for $g\in V_f$ if all folds are non-degenerate, tha…

Global-equivalence conjecture. The same equivalence, or a similar one, may also work for the case $m=1,n=2$.

Consider a fast-slow partially hyperbolic system with small parameter $\varepsilon$, in the case where the averaged slow motion is a rotation because the averaged vector field has…

Bounded-component conjecture. On this interval,

Consider a fast-slow system satisfying assumptions (C1)–(C6), with a chaotic invariant set near $S_a^+(\delta) \cup \alpha^+(\delta) \cup S_a^-(\delta) \cup \alpha^-(\delta)$ as gi…