The Monodromy Group

Henryk Żołądek

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English

Birkhauser Verlag AG
11 May 2025

Algebra; Complex analysis, complex variables; Functional analysis & transforms; Differential calculus & equations; Algebraic topology

Series: Monografie Matematyczne

This book presents the monodromy group, underlining the unifying role it plays in a variety of theories and mathematical areas. In singularity theory and algebraic geometry, the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures. In the theory of systems of linear differential equations, one has the Riemann-Hilbert problem, the Stokes phenomena and the hypergeometric functions with their multidimensional generalizations. In the theory of homomorphic foliations, there appear the Ecalle-Voronin-Martinet-Ramis moduli. Moreover, there is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions.

The material is addressed to a wide audience, ranging from specialists in the theory of ordinary differential equations to algebraic geometers. Readers will quickly get introduced to modern and vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic foliations, Galois theory, and parts of algebraic geometry, without searching in vast literature.

This second edition has been enlarged by several sections, presenting new results appeared since the first edition.

By: Henryk Żołądek
Imprint: Birkhauser Verlag AG
Country of Publication: Switzerland
Edition: Second Edition 2025
Volume: 67
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9783031912696
ISBN 10: 3031912691
Series: Monografie Matematyczne
Pages: 687
Publication Date: 11 May 2025
Audience: Professional and scholarly , College/higher education , Undergraduate , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Henryk Żołądek is a Polish mathematician and a professor of mathematical sciences. He specializes in mathematical physics and differential equations.