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The coefficients of series expansions of integrals, the weight and Hodge filtrations and the spectrum of a critical point

  • V. I. Arnold
  • S. M. Gusein-Zade
  • A. N. Varchenko
Chapter
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

Let us consider the integral of a holomorphic differential form over a homology class of a continuous family of integral homologies of fibres of the Milnor fibration ofa critical point. The function given by the integral can be expanded in a series ofpowers ofthe parameter and powers ofthe logarithm ofthe parameter ofthe family (Chapter 1O). Each coefficient ofthe series depends linearly both on the form and on the continuous family ofintegral homologies.

Keywords

Principal Part Hodge Structure Jordan Block Holomorphic Form Weight Filtration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • V. I. Arnold
  • S. M. Gusein-Zade
    • 1
  • A. N. Varchenko
    • 2
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Department of MathematicsThe University of North Carolina at Chapel HillChapel HillUSA

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