Linked Questions
10 questions linked to/from Lifting a quadratic system to a non-vanishing vector field on $S^{3}$ or $T^{1} S^{2}$
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Proposals for polymath projects
Background
Polymath projects are a form of open Internet collaboration aimed towards a major mathematical goal, usually to settle a major mathematical problem. This is a concept introduced in 2009 by ...
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Can the Laplace operator on $n-$ manifolds be represented as a sum of $n$ second order derivational operators
EDIT: According to some comments on this post I revise the title to remove the misunderestanding.
Assume that $M$ is a Riemannian manifold of dimension $n$. The natural Laplace operator associated ...
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11
votes
2
answers
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Elliptic operators corresponds to non vanishing vector fields
Added, June 19, 2019: The main motivation of this post is to associate an index to differential operator associated to a dynamical system such that the index has an interesting ...
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4
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1
answer
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A special non vanishing vector field on $S^{3}$
Is there a non vanishing vector field on $S^{3}$ with an infinite family $T_{\lambda}$ of invariant torus such that each $T_{\lambda}$ has an structure of a Kronecker foliation but for ...
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13
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Hilbert 16th problem and dynamical Lefschetz trace formula
I would like to apply the known version of the conjectural formula (11) page 10 of the paper Number theory and dynamical Lefschetz trace formula.
Disclaimer: I do not have a complete ...
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A question on tangent bundle (and second tangent bundle)
Let $M$ be a $n$ dimensional manifold and $p:TM\to M$ be the projection map. Then $\ker Dp$ is a $n$ dimensional vector bundle on $TM$, as a sub bundle of $TT(M)$.
For what type of manifolds, $...
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2
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answers
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Why Poincare sphere compactification and not torus compactification
The Poincare compactification is a method to carry a polynomial vector field on the plane to an analytic vector field on $S^{2}$ via analytic embedding $$(x,y)\to (\frac{x}{\sqrt{1+x^{2}+y^{2}}},\...
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2
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answer
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Divergence invariant lifting of a vector field via a submersion
What is an example of a smooth submersion $P:S^{3}\to S^{2}$ for which the following statment is Not true:
For every vector field $X$ on $S^{2}$ there is a non vanishing vector field $\tilde{X}$...
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A (different) foliation arising from Hopf fibration
In this question, first we fix an isomorphism between $TS^{3}$ and $S^{3}\times \mathbb{R}^{3}$.(To be more precise we consider the global trivialization of $TS^{3}$ with help of $3$ global ...
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Irrational closed orbits of vector fields on $S^2$ (Limit cycles and trace formula)
Motivations: We first introduce our motivations: We wish to find an operator-theoretical interpretation for the number of limit cycles of a polynomial vector field on the plane. We quote the ...
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