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4
questions
3
votes
0
answers
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Progess on conjectures of Palis
I came across a "A Global Perspective for Non-Conservative Dynamics" by Palis. He has some conjectures
"Global Conjecture:
There is a dense set $D$ of dynamics such that any element of ...
- 227
0
votes
0
answers
37
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Generic non-existence of 1. Integral of continuous DS
Let $M$ be a compact manfiold and $F \in \mathcal{X}(M)$. We define a DS on $M$ by
$$\dot{\mathbf{x}}=F(\mathbf{x}(t))$$
In 1 it was shown by Hurley, that a generic diffeomorphism on $M$ does not have ...
- 227
0
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0
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290
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Proof that a first integral is not a constant function
Let $U$ be an (open) set in $\mathbb{R}^n$. And we are given a set of $m$ basis functions
$$B=\{\psi_i(x): U \rightarrow \mathbb{R}\mid i=1,\ldots,m \}$$
such that all of them are differentiable and ...
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1
vote
0
answers
179
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Subset of the domain of attraction
Let $x \in R^n$ and $f : R^n \to R^n$, $f\in C^1$
$$
\frac{\mathrm{d}}{\mathrm{d}t} x(t) = f(x(t))
$$
be such that $f(0) = 0$ is asymptotically stable. The domain of attraction is the set of initial ...
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