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Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.

3 votes

Continuity of the period for a periodic dynamical system

For $n = 2$, the answer is Yes. Topological considerations (as in the proof of the Poincare-Bendixson theorem) mean that the first-return map for a transversal to a point on a periodic orbit will be t …
Martin M. W.'s user avatar
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3 votes
Accepted

Planar flow with bounded orbits and a single equilibrium point

(edited to include Willie Wong's idea for $C^0$ case.) This kind of flow can't exist in any dimension. Let $S$ be the unit sphere and $B$ be the open unit ball. If the origin is a global attractor for …
Martin M. W.'s user avatar
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3 votes

Why is the largest invariant set the following?

Here's how I interpret that paper. Why (1,1,1,1) is special First, to make things simpler, I'll rewrite the equations by collapsing some constants as follows. $x' = x[a(\frac{1}{x} - z) + b(\frac{1}{x …
Martin M. W.'s user avatar
  • 6,571
5 votes
Accepted

Can orientation preserving diffeomorphism in $\mathbb{R}^d$ be presented by flowmap of dynam...

No, this is usually not possible. There's a previous MO question discussing this, but to add to the material there: A time-one map $\phi_1$ commutes with the 1-parameter family of diffeomorphisms $\p …
Martin M. W.'s user avatar
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