Question

How to show that a map is a diffeomorphism?

score 1.2k · Answer 1 · 2017-12-09 14:41:59

1.2k

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How to show that a map is a diffeomorphism?

Published on 09 Dec 2017 - 14:41

score 51 · Answer 2 · 2017-12-14 08:37:51

51

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How to define this diffeomorphism properly and how to clean up notation as to be more canonical?

Published on 14 Dec 2017 - 8:37

score 563 · Answer 3 · 2017-12-14 14:47:21

563

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Diffeomorphism from the real line to itself.

Published on 14 Dec 2017 - 14:47

score 207 · Answer 4 · 2026-03-26 09:25:50

207

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Coordinates on $SU(2)$

Published on 26 Mar 2026 - 9:25

score 368 · Answer 5 · 2018-01-12 00:18:41

368

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Show $x\mapsto x/\sqrt{1+\vert x\vert^2}$ is diffeomorphism

Published on 12 Jan 2018 - 0:18

score 6.5k · Answer 6 · 2011-07-27 21:06:20

6.5k

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No diffeomorphism that takes unit circle to unit square

Published on 27 Jul 2011 - 21:06

score 4.6k · Answer 7 · 2013-03-04 15:30:58

4.6k

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Using tan(x), show that open interval is diffeomorphic with the real line

Published on 04 Mar 2013 - 15:30

score 89 · Answer 8 · 2026-03-12 17:07:10

89

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If $\phi$ is a homeomorphism and both $\phi$ and $\phi^{-1}$ extend to differentiable functions, is ${\rm D}\phi(x)$ invertible?

Published on 12 Mar 2026 - 17:07

score 75 · Answer 9 · 2020-08-04 18:48:33

75

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Characterization of $C^\alpha$-differentiability on a submanifold with boundary

Published on 04 Aug 2020 - 18:48

score 77 · Answer 10 · 2020-08-10 21:19:00

77

Views

Diffeomorphisms that permute angles?

Published on 10 Aug 2020 - 21:19

score 32 · Answer 11 · 2020-08-12 08:51:11

32

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If $T_t$ is a family of diffeomorphisms on $U$ and $V_2⊆U$ is open, is there an open set $V_1⊆U$ with $T_t(V_1)⊆V_2$ for $t$ sufficiently small?

Published on 12 Aug 2020 - 8:51

score 36 · Answer 12 · 2020-08-12 19:15:59

36

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Conditions on $v:[0,\tau]\times U\to\mathbb R^d$ that ensure that the solution to ${\rm d}X(t)=v(t,X(t)){\rm d}t$ maps into $U$

Published on 12 Aug 2020 - 19:15

score 686 · Answer 13 · 2020-08-14 12:19:49

686

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Any diffeomorphism can be locally factorised with several primitive diffeomorphisms.

Published on 14 Aug 2020 - 12:19

score 40 · Answer 14 · 2020-08-15 09:45:00

40

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Chapman-Kolmogorov equations for $X^{s,\:x}(t)=x+\int_s^tv\left(r,X^{s,\:x}(r)\right)\:{\rm d}r$

Published on 15 Aug 2020 - 9:45

score 272 · Answer 15 · 2020-08-16 15:00:25

272

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Lee Smooth Manifolds Proposition 2.15 - What is a product of diffeomorphisms?

Published on 16 Aug 2020 - 15:00

List Question

How to show that a map is a diffeomorphism?

How to define this diffeomorphism properly and how to clean up notation as to be more canonical?

Diffeomorphism from the real line to itself.

Coordinates on $SU(2)$

Show $x\mapsto x/\sqrt{1+\vert x\vert^2}$ is diffeomorphism

No diffeomorphism that takes unit circle to unit square

Using tan(x), show that open interval is diffeomorphic with the real line

If $\phi$ is a homeomorphism and both $\phi$ and $\phi^{-1}$ extend to differentiable functions, is ${\rm D}\phi(x)$ invertible?

Characterization of $C^\alpha$-differentiability on a submanifold with boundary

Diffeomorphisms that permute angles?

If $T_t$ is a family of diffeomorphisms on $U$ and $V_2⊆U$ is open, is there an open set $V_1⊆U$ with $T_t(V_1)⊆V_2$ for $t$ sufficiently small?

Conditions on $v:[0,\tau]\times U\to\mathbb R^d$ that ensure that the solution to ${\rm d}X(t)=v(t,X(t)){\rm d}t$ maps into $U$

Any diffeomorphism can be locally factorised with several primitive diffeomorphisms.

Chapman-Kolmogorov equations for $X^{s,\:x}(t)=x+\int_s^tv\left(r,X^{s,\:x}(r)\right)\:{\rm d}r$

Lee Smooth Manifolds Proposition 2.15 - What is a product of diffeomorphisms?

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