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| eBook ISBN: | 978-1-4704-5654-2 |
| Product Code: | MEMO/263/1273.E |
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| MAA Member Price: | $76.50 |
| AMS Member Price: | $51.00 |
| Softcover ISBN: | 978-1-4704-4069-5 |
| eBook: ISBN: | 978-1-4704-5654-2 |
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| AMS Member Price: | $102.00 $76.50 |
| Softcover ISBN: | 978-1-4704-4069-5 |
| Product Code: | MEMO/263/1273 |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $51.00 |
| eBook ISBN: | 978-1-4704-5654-2 |
| Product Code: | MEMO/263/1273.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $51.00 |
| Softcover ISBN: | 978-1-4704-4069-5 |
| eBook ISBN: | 978-1-4704-5654-2 |
| Product Code: | MEMO/263/1273.B |
| List Price: | $170.00 $127.50 |
| MAA Member Price: | $153.00 $114.75 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 263; 2020; 171 ppMSC: Primary 76; 37; Secondary 35
The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable \(x\)) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
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Table of Contents
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Chapters
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1. Introduction and main result
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2. Functional setting
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3. Transversality properties of degenerate KAM theory
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4. Nash-Moser theorem and measure estimates
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5. Approximate inverse
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6. The linearized operator in the normal directions
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7. Almost diagonalization and invertibility of $ {\mathcal L}_\omega $
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8. The Nash-Moser iteration
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A. Tame estimates for the flow of pseudo-PDEs
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Additional Material
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable \(x\)) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
-
Chapters
-
1. Introduction and main result
-
2. Functional setting
-
3. Transversality properties of degenerate KAM theory
-
4. Nash-Moser theorem and measure estimates
-
5. Approximate inverse
-
6. The linearized operator in the normal directions
-
7. Almost diagonalization and invertibility of $ {\mathcal L}_\omega $
-
8. The Nash-Moser iteration
-
A. Tame estimates for the flow of pseudo-PDEs
