Table of contents

CONTENTS Chapter I. Analytic functionals § 1. Defining sets of analytic functionals § 2. Subharmonic functions § 3. Laplace transform of analytic functionals § 4. Convolution operators Chapter II. Surjectivity of convolution operators in the one-dimensional case § 5. A review of studies on the problem of the surjectivity of convolution operators § 6. Solvability of non-homogeneous convolution equations in convex domains in the complex plane Chapter III. Surjectivity of convolution operators in the multidimensional case § 7. Geometry of a convex domain § 8. Construction of a special entire function which is not of completely regular growth § 9. Estimates of indicators of subharmonic functions §10. A solvability criterion for non-homogeneous convolution equations in convex domains in Chapter IV. Homogeneous convolution equations §11. Approximation of subharmonic and plurisubharmonic functions §12. Polynomial approximation of entire functions §13. Approximation of solutions of a homogeneous convolution equation §14. Extension of solutions of a homogeneous convolution equation References

CONTENTS Chapter I. Introduction Chapter II. Stability in the neighbourhood of a periodic torus Chapter III. Stability for arbitrary initial conditions Chapter IV. Transpositions, applications, prospects §1. Additional variables and an application to celestial mechanics §2. Transposition to other contexts and degenerate cases §3. Systems with (infinitely) many degrees of freedom §4. Steepness, quasi-convexity, and closed orbits Chapter V. Robust tori; Arnol'd diffusion §1. Robust tori and "normalization" §2. Arnol'd diffusion Appendix 1. Some Diophantine approximation Appendix 2. Gevrey asymptotic expansions References

CONTENTS Introduction § 1. Main theorems Chapter I. Algebra § 2. Moyal deformations of the Poisson bracket and *-product on § 3. Algebraic construction § 4. Central extensions § 5. Examples Chapter II. Deformations of the Poisson bracket and *-product on an arbitrary symplectic manifold § 6. Formal deformations: definitions § 7. Graded Lie algebras as a means of describing deformations § 8. Cohomology computations and their consequences § 9. Existence of a *-product Chapter III. Extensions of the Lie algebra of contact vector fields on an arbitrary contact manifold §10. Lagrange bracket §11. Extensions and modules of tensor fields Appendix 1. Extensions of the Lie algebra of differential operators Appendix 2. Examples of equations of Korteweg-de Vries type References