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Results tagged with ca.classical-analysis-and-odes
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user 514043
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
0
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2
answers
69
views
Is the right-hand term of the dynamic system equivalent to the original system after being m...
Given two dynamical systems where $f$ is lipschitz for $x$ : $\begin{cases} x'(t)=af(x,t),\\ x(0)=x_0,\end{cases} t\in[0,\tau]$ and $\begin{cases} z'(t)=f(z,t),\\ z(0)=x_0,\end{cases} t\in[0,\tau']$, …
- 109
-1
votes
1
answer
157
views
Can we use linear map to approximate lipschitz continuous function $f$ in a compact domain a...
Suppose $f : \mathbb{R}\to \mathbb{R}$ is lipschitz continuous function , $K$ is a compact domain, for any $\varepsilon>0$, can we find $d,a\neq 0,c,w,b \in \mathbb{R}$ such that $\|df(ax+c)-(wx+b)\|< …
- 109
0
votes
1
answer
39
views
Is the right-hand term of the autonomous dynamic system equivalent to the original system af...
Given two dynamical systems where $f$ is lipschitz for $x$ : $\begin{cases} x'(t)=af(x),\\ x(0)=x_0,\end{cases} t\in[0,\tau]$ and $\begin{cases} z'(t)=f(z),\\ z(0)=x_0,\end{cases} t\in[0,\tau']$, and …
- 109
0
votes
1
answer
113
views
Can orientation preserving diffeomorphism in $\mathbb{R}^d$ be presented by flowmap of dynam...
Because flowmaps are homeomorphic maps on a compact domain $\Omega$, I was wondering if there is any literature that proves that diffeomorphism $\Phi(x)$ can be expressed as a flowmap of a certain dyn …
- 109
-2
votes
1
answer
203
views
If a continuous function is differentiable at a point, is it differentiable in some neighbor... [closed]
This seems like it should be true but I was wondering if anyone could prove it. Thanks!
- 109
1
vote
1
answer
188
views
Can orientation preserving diffeomorphism in $\mathbb{R}^d$ be presented by flowmap of dynam...
Because flowmaps are homeomorphic maps, I was wondering if there is any literature that proves that diffeomorphism $\Phi(x)$ can be expressed as a flowmap of a certain dynamical system?
that is, does …
- 109
2
votes
1
answer
114
views
Any theorem shows that flowmap $\phi_{\sum_{i=1}^n a_i f_i(x)}^\tau$ can be approximated by ...
Given a control family $F:=\{f_1,\dotsc,f_n\}$, and $\phi_f^\tau(x)$ is the flowmap of the dynamical system
$$
\begin{cases}
z'(t)=f(z),\\
z(0)=x,
\end{cases}
$$ at end time point $\tau$.
Suppose $a_i …
- 109