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li ang Duan
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revised
Can orientation preserving diffeomorphism in $\mathbb{R}^d$ be presented by flowmap of dynamical systems? (time-varying case)
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asked
Can orientation preserving diffeomorphism in $\mathbb{R}^d$ be presented by flowmap of dynamical systems? (time-varying case)
revised
Can orientation preserving diffeomorphism in $\mathbb{R}^d$ be presented by flowmap of dynamical systems?
[Edit removed during grace period]
accepted
Can orientation preserving diffeomorphism in $\mathbb{R}^d$ be presented by flowmap of dynamical systems?
comment
Can orientation preserving diffeomorphism in $\mathbb{R}^d$ be presented by flowmap of dynamical systems?
Thanks! But I found a paper that shows diffeomorphism can be approximated by flowmaps, do you have any comments on this paper? sciencedirect.com/science/article/pii/S1474667016448974 This seems to contradict the chaos you mentioned.
asked
Can orientation preserving diffeomorphism in $\mathbb{R}^d$ be presented by flowmap of dynamical systems?
awarded
 Commentator
comment
If a continuous function is differentiable at a point, is it differentiable in some neighborhood around that point?
Thanks! I have one more question, how about Lipschitz continuous function which is differentiable almost everywhere? If a Lipschitz continuous function is differentiable at a point, is it differentiable in some neighborhood around that point?
asked
If a continuous function is differentiable at a point, is it differentiable in some neighborhood around that point?
comment
Any theorem shows that flowmap $\phi_{\sum_{i=1}^n a_i f_i(x)}^\tau$ can be approximated by $\phi_{f_{\theta(t)}(x)}^{\tau'}$?
you can check this simply one: webspace.science.uu.nl/~frank011/Classes/numwisk/ch13.pdf
accepted
Any theorem shows that flowmap $\phi_{\sum_{i=1}^n a_i f_i(x)}^\tau$ can be approximated by $\phi_{f_{\theta(t)}(x)}^{\tau'}$?
comment
Any theorem shows that flowmap $\phi_{\sum_{i=1}^n a_i f_i(x)}^\tau$ can be approximated by $\phi_{f_{\theta(t)}(x)}^{\tau'}$?
Thanks for your answer, recently I found that the splitting method can solve the problem immediately. But your method is also very inspiring to me！
comment
Any theorem shows that flowmap $\phi_{\sum_{i=1}^n a_i f_i(x)}^\tau$ can be approximated by $\phi_{f_{\theta(t)}(x)}^{\tau'}$?
The proof seems to be fine, but is it too strong to assume $T\in (0, min(1/𝐿,𝑏/𝑀)) $? So that it does not meet the conditions of this proposition (the proposition does not limit the range of T values)
asked
How expressive is $e^A$ in the sense of universal approximation?
revised
Any theorem shows that flowmap $\phi_{\sum_{i=1}^n a_i f_i(x)}^\tau$ can be approximated by $\phi_{f_{\theta(t)}(x)}^{\tau'}$?
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asked
Any theorem shows that flowmap $\phi_{\sum_{i=1}^n a_i f_i(x)}^\tau$ can be approximated by $\phi_{f_{\theta(t)}(x)}^{\tau'}$?
comment
Can we use linear map to approximate lipschitz continuous function $f$ in a compact domain after some linear transform?
The answer should be no, if Lipschitz function $f(x)$ is a piecewise linear function with slopes {1,2,1/2,1}, we cannot deal with the breakpoint $x_{b}$.
accepted
Is the right-hand term of the autonomous dynamic system equivalent to the original system after being multiplied by a constant?
awarded
 Scholar
comment
Is the right-hand term of the dynamic system equivalent to the original system after being multiplied by a constant?
I have accepted your answer, thank you very much
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