6 problems

Minkowski dimension conjecture. Any such spiral trajectory has Minkowski dimension

Let $\varepsilon$ and $\delta$ be positive perturbation parameters, and suppose that the assumptions concerning the parameters and reduced flow hold. Assume that the singularities of…

Let the assumptions concerning the parameters, reduced flow, and slow drift hold, and suppose that the singularities of the system are remote. Let $\theta$ denote the system parame…

Let $H(z,\varepsilon)$ be a vector field satisfying Assumptions --, with slow manifold $S_{\varepsilon}$ and linear fast fibers $\mathcal{N}_{\varepsilon}(p)$ at basepoints…

Let $f\in C^{1}(\mathbb{R})$ satisfy conditions (H1)–(H3), and let $\beta$ be the balance point. Consider initial histories satisfying $x(\theta)\in[\chi^{-},\chi^{+}]$ for…

Canard-cycle conjecture. For every desired number $l\in\mathbb{N}$ there exists a local topologically generic set of systems such that the slow curve is nondegenerate and simple un…