Mathematics Problem Archive

Let $f$ be holomorphic in the unit disk with a simple zero at $0$, exactly two simple $1$-points at $b$ and $-b$, and no other zeros or $1$-points. De...

For the classical polynomial Liénard system $$\dot x=y-F(x),\qquad \dot y=-x,$$ let $\operatorname{Lie}(n)$ be the maximum number of limit cycles when...

Are there smooth vector fields in $\mathbb{R}^3$ satisfying the hypotheses of the Markus–Yamabe conjecture and having periodic orbits?...

For $n\in\mathbb{N}$, let $\Pi(n)$ be the product of its decimal digits, and let $\operatorname{Pm}(n)$ be the least positive integer such that $\Pi^{...

Given a C∞ metric in a neighborhood of a point in a 2-dimensional Riemannian manifold, does there exist an isometric embedding of some neighborhood of...

Do non-singular real plane projective curves of an odd degree consisting of a single connected component form a connected set (i.e., are they rigid is...

Is it true that any component of the complement of the discriminant variety of a versal deformation contains a Morsification, whose all $\mu(f)$ criti...