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9781470475062 Academic Inspection Copy

KAM Theory for Active Scalar Equations

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The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
Zineb Hassainia, New York University in Abu Dhabi, United Arab Emirates, and Courant Institute of Mathematical Sciences, New York University, New York. Taoufik Hmidi, New York University in Abu Dhabi, United Arab Emirates, and Courant Institute of Mathematical Sciences, New York University, New York. Nader Masmoudi, New York University in Abu Dhabi, United Emirates, and Courant Institute of Mathematical Sciences, New York University, New York.
1. Introduction 2. Hamiltonian reformulation 3. Linearization and frequencies structure 4. Functional tools 5. Hamiltonian toolbox 6. Berti-Bolle approach for the approximate inverse 7. Toroidal pseudo-differential operators 8. New approach related to Egorov theorem 9. Reducibility of the linearized operator 10. Proof of the main result A.
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