Timeline for Why do unstable manifolds of two close point intersect each other in Baker map?
Current License: CC BY-SA 4.0
26 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
|
|
| May 19, 2019 at 13:12 | comment | added | Anthony Quas | The point is that for most $x$ and $y$, $y$ does not lie in the unstable manifold of $x$ (otherwise the unstable manifold would be of the wrong dimension). This implies (as I showed above) that there is no $t$ lying in the intersection of the unstable manifolds. | |
| May 19, 2019 at 11:56 | comment | added | Adam | I am really interested to know what is mathematic reason in nonlinear Baker, two unstable manifold intersect each other. | |
| May 19, 2019 at 11:55 | comment | added | Adam | @AnthonyQuas: It doesn't mean they intersect each other, does it? because maybe they are very close to each other. | |
| May 19, 2019 at 5:14 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 4.0 |
might be confusing - it is not anybody's name
|
| May 19, 2019 at 0:33 | comment | added | Anthony Quas | If $t\in W^u(x)\cap W^u(y)$, then $d(f^{-n}t,f^{-n}x)\to 0$ and $d(f^{-n}t,f^{-n}y)\to 0$, so that $d(f^{-n}x),f^{-n}y)\to 0$. Of course this is not the case for typical nearby $x$ and $y$. | |
| May 18, 2019 at 23:43 | comment | added | Adam | @Mike Miller. You're right. I modified the question. I'm looking for a map that defines on $ S^1 \times [-1, 1]$ | |
| May 18, 2019 at 23:40 | history | edited | Adam | CC BY-SA 4.0 |
deleted 6 characters in body
|
| May 18, 2019 at 22:19 | comment | added | mme | The link by Lee Mosher is for a map on the unit disc, not some arbitrary Riemannian manifold. You're asking for that specific map? | |
| May 18, 2019 at 22:08 | history | edited | Adam | CC BY-SA 4.0 |
edited title
|
| May 18, 2019 at 15:47 | comment | added | Adam | @LeeMosher : I understood stable and unstable manifold intersect each other but I would like to know why unstable manifolds intersect each other. I will appreciate if you help me or introduce some references. | |
| May 18, 2019 at 15:45 | comment | added | Adam | @LeeMosher : Yes, But I asked why unstable manifold $W_{x}^{u}$ and $W_{y}^{y}$ intersect each other. And then, why it is unique? | |
| May 18, 2019 at 15:43 | history | edited | Adam | CC BY-SA 4.0 |
added 47 characters in body
|
| May 18, 2019 at 15:40 | comment | added | Lee Mosher | Perhaps you can provide a definition or a link to a "Baker map". I know what the Baker's map is, but presumably that is not what you mean because its stable and unstable manifolds do indeed have a local product structure. | |
| S May 18, 2019 at 15:39 | history | edited | Adam | CC BY-SA 4.0 |
added 75 characters in body
|
| S May 18, 2019 at 15:39 | history | suggested | Michal | CC BY-SA 4.0 |
added 75 characters in body
|
| May 18, 2019 at 15:37 | review | Suggested edits | |||
| S May 18, 2019 at 15:39 | |||||
| May 18, 2019 at 15:32 | comment | added | Adam | @AnthonyQuas : Thanks for your comment. No, I know when we have local product structure stable and unstable manifold intersect each other . But as I said I want to show that unstable manifolds intersect each other in Baker map. We see they intersect each other when we draw it but I do not know how I can prove it. | |
| May 18, 2019 at 15:30 | comment | added | Adam | @LeeMosher : Thanks for your comment. I forgot to write map is Baker. When we draw picture we will see their unstable manifold intersect each other but I can not prove it | |
| May 18, 2019 at 10:12 | history | edited | Adam | CC BY-SA 4.0 |
deleted 12 characters in body
|
| S May 18, 2019 at 10:01 | history | suggested | user64494 | CC BY-SA 4.0 |
The title is improved.
|
| May 18, 2019 at 9:59 | review | Suggested edits | |||
| S May 18, 2019 at 10:01 | |||||
| May 18, 2019 at 9:56 | history | edited | Adam | CC BY-SA 4.0 |
added 7 characters in body
|
| May 18, 2019 at 1:16 | comment | added | Anthony Quas | Is the result you want that (under some conditions) the stable manifold of $x$ meets the unstable manifold of $y$? | |
| May 18, 2019 at 0:43 | comment | added | Lee Mosher | It's not true. In fact if we assume that $f$ is Anosov then locally the stable manifolds form a decomposition, hence the only way that that $W^u_x$ and $W^u_y$ can have nonempty intersection is if they are equal. Are you sure you wrote the question correctly? | |
| May 18, 2019 at 0:23 | history | asked | Adam | CC BY-SA 4.0 |