4 problems

Global stability conjecture. Suppose all eigenvalues of $A_L$ and $A_R$ have negative real part. If $H(y_1)$ is an asymptotically stable equilibrium of the limiting fast system for…

Consider two-dimensional piecewise-linear continuous ordinary differential equation systems in scenarios for which an attracting annulus has been proved to exist. Lum and Chua's co…

Let $g: \mathbb{R}^d \to \mathbb{R}^d$ be continuous and linearly homogeneous. Let $f: \mathbb{R}^d \to \mathbb{R}^d$ be continuous and satisfy … A fixed point is Lyapunov stable i…

Bounded-distortion periodicity conjecture. The separation property is unnecessary to obtain $C^2$ genericity of the periodic behavior.