All Questions
5
questions
3
votes
2
answers
296
views
Inverse limit space and $C^1$ topology
Let $f_n$ be a sequence of $C^1$-maps on closed manifold $M$. If $f_n \to f$ in $C^1$-topology. Does $M_{f_n}$ converges to $M_f$ in the Hausdorff distance?
We define $M(f)=\{\bar{x}=(x_j) \in M^{\...
3
votes
0
answers
85
views
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
views
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
votes
0
answers
290
views
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 ...
- 227
0
votes
0
answers
69
views
Example of DS with a dense trajectory in the whole state space
Let $U \subset \mathbb{R}^n$ be an open and connected set. We assume there is a vector field $F \in \mathcal{C}^1(\overline{U})$ giving rise to a DS ($\overline{U}$ denotes the closure)
$$\dot{\mathbf{...
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