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Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.

6 votes

Knots and Dynamics. Recent breakthroughs?

There are certainly plenty of connections between knot theory and dynamical systems. On the fairly physical end of things, there was a recent workshop you might find interesting: http://www.kitp.uc …
Ryan Budney's user avatar
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9 votes

nowhere vanishing vector field on a manifold

If there is a 1-dimensional sub-bundle of $TM$, if it was an orientable bundle you'd have $\chi M = 0$. Consider the case it's non-orientable. Then there would be a 2-sheeted connected "orientation …
Ryan Budney's user avatar
  • 44.3k
7 votes
Accepted

How can generic closed geodesics on surfaces of negative curvature be constructed?

If you think of your surface as the upper half plane modulo a group of Moebius transformations $G$, start by representing each of your Moebius transformations $ z \longmapsto \frac{az+b}{cz+d}$ by a M …
Ryan Budney's user avatar
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3 votes

Codimension zero immersions

Smale-Hirsch is not just a theorem about existence of immersions. It's a theorem about the homotopy-type of the space of all immersions. Given an immersion $$S^{n-1} \to \mathbb R^n$$ you get a bu …
Ryan Budney's user avatar
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