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The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.

1 vote
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65 views

What *piecewise* smooth curves/surfaces/hypersurfaces give rise to forward-invariant regions...

Consider a set $\mathcal{B}\subset \mathbb{R}^n$ that is homeomorphic to a closed n-dimensional ball, and denote its boundary by $\mathcal{H}$. Assume that $\mathcal{H}$ is a "piecewise smooth" hypers …
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3 votes
0 answers
140 views

What is known about topological equivalence of polynomial dynamical systems on two different...

The question is mainly about $\it flows$, not maps (i.e., continuous time, not discrete time). Is it known if the study of polynomial dynamical systems on $\mathbb R^n$ can be reduced to the study o …
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