Timeline for A criterion on a vector field for its flow to extend continuously at $t=\infty$
Current License: CC BY-SA 4.0
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| Aug 26, 2019 at 15:16 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Aug 26, 2019 at 13:17 | comment | added | Iosif Pinelis | @PascalLambrechts : Since you mentioned a homotopy in your post, I did suspect that actually you also needed the continuity of the extension in the initial position $x$. But, as you note, that also quickly follows from the answer. Anyhow, I am glad the answer made you happy. :-) | |
| Aug 26, 2019 at 6:22 | vote | accept | Pascal Lambrechts | ||
| Aug 26, 2019 at 6:21 | comment | added | Pascal Lambrechts | thank you for the answer ! Actually I also need the continuity of the extension at $T=\infty$ to be continuous w.r.t to $x$. But I see that this follows from the inequality in the displaymath after (4), which implies that $$\|y_\infty-y_t\|\leq \frac{1-r_t}{C},$$ and from the continuity for $T<\infty$ which follows from the lipschitz hypothesis on V. So this is exactly what I needed and makes me happy :-) | |
| Aug 26, 2019 at 3:38 | comment | added | Iosif Pinelis | The solution is now fully formalized, streamlined, and simplified. | |
| Aug 26, 2019 at 3:36 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Aug 26, 2019 at 3:23 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Aug 25, 2019 at 19:39 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Aug 25, 2019 at 12:04 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Aug 25, 2019 at 5:18 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Aug 25, 2019 at 4:43 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Aug 25, 2019 at 4:08 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Aug 25, 2019 at 3:57 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Aug 25, 2019 at 3:22 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |