Linked Questions
17 questions linked to/from Limit cycles as closed geodesics (in negatively or positively curved space)
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Flat Riemannian metrics adapted to quadratic vector fields with center
Assume that $P(x,y),Q(x,y)\in \mathbb{R}[x,y]$ are two polynomials of degree $2$ with $P(0,0)=Q(0,0)=0.$
Suppose that the vector field $$\begin{cases} x'=P(x,y)\\ y'=Q(x,y) \end{cases}$$ has a center ...
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An isocline geodesic characterization of $2$ dimensional flat metrics
Lets we have a Riemannian metric on an open subset of the plane which satisfies the following local property.
Local Property: For every point $x$ and every foliation by geodesics around $x$, ...
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