10 problems

A quadratic center is a center of a planar quadratic differential system, and a critical period is a maximum or minimum of its period function. Chicone's conjecture. Every quadrati…

Consider the Loud normal form … and let $\Gamma_U$ denote the subset of parameter space left unspecified in the cited bifurcation analysis. A parameter is regular when the correspo…

Let $\ddot{x}+g(x)=0$ be a potential system with potential energy $G(x)$, where $G$ is even, and let the system have a center at the origin. Even-potential critical-period conjectu…

Let $\Delta$ be the germ of an interior local-bifurcation curve at $\nu=(-2,2)$, and let $\delta_1$ be the germ of an interior local-bifurcation curve at the Loud parameter…

Let $\Delta$ and $\delta_3$ be germs of curves contained in the local bifurcation set of the period function at the interior of the period annulus. A parameter region is one with e…

Let a quadratic center have a period annulus with an outer boundary, and define its criticality at the outer boundary as the maximal number of critical periodic orbits produced the…

Among quadratic centers, let $L_1,L_2,L_3$ be the three Loud parameter values at which the inner-boundary criticality attains its maximum value two. A twin pair consists of a Loud…

Chicone's Loud normal form conjecture. If a quadratic differential system has a center with a period function that is not monotonic, then an affine transformation and a constant re…

Criticality-one conjecture. For parameters on the bifurcation curve with $F_0\in(\tfrac{9}{8},\tfrac{6}{5})$ or $F_0\in(1,\tfrac{9}{8}]$ satisfying the remaining hypotheses of the…

Comparison conjecture. The space of $1$-eigenfunctions of the meromorphic extension of $mathcal L_{H,s}^{+}$ is linearly isomorphic to…