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Results tagged with differential-equations
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user 1227
Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
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 …
- 6,571
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 …
- 6,571
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 …
- 6,571
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 …
- 6,571