Table of contents

CONTENTS Introduction § 1. A short review of results § 2. Criteria for Fuchsian systems with regular singular points § 3. Preliminary information. The method of solution § 4. The solubility of the Riemann-Hilbert problem for an irreducible representation of dimension three § 5. Fuchsian systems of two equations on the Riemann sphere. The Fuchsian weight of a representation § 6. The Riemann-Hilbert problem for a system of three equations § 7. The Fuchsian weight and two-dimensional holomorphic vector bundles on the Riemann sphere Conclusion References

CONTENTS § 1. Introduction § 2. Realizability theorem § 3. Tagged skeletons § 4. Coding integrable Hamiltonian systems References

CONTENTS Preface Chapter I. The analytic theory Introduction § 1. The Cauchy problem in spaces (the case of cylindrical evolution) § 2. The Cauchy problem in spaces (the case of conical evolution) § 3. The adjoint problem Chapter II. The exponential theory Introduction § 1. The Cauchy problem in the scale § 2. The Cauchy problem in the scale § 3. The adjoint problem Chapter III. The connection between the analytic theory and the exponential theory Introduction § 1. Pseudodifferential operators with complex arguments § 2. The Cauchy problem for pseudodifferential equations § 3. Fourier transformation of analytic functions § 4. The fundamental diagram. Concluding section (the connection between the analytic and exponential theories) References

CONTENTS Introduction § 1. Expansion of monodromy transformations of class 1 into terms with incommensurable rates of decrease § 2. Function-theoretic properties of simple and sectorial cochains § 3. The Phragmén-Lindelöf theorem for simple and sectorial cochains § 4. Superaccurate asymptotic series Appendix I Appendix II Historical comments References