Skip to main content
EXTENDED SEARCH
Log in
Top
Published in:
Read chapter Read first chapter

2016 | OriginalPaper | Chapter

15. Abelian Integrals: From the Tangential 16th Hilbert Problem to the Spherical Pendulum

Authors : Pavao Mardešić, Dominique Sugny, Léo Van Damme

Published in: Mathematical Sciences with Multidisciplinary Applications

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this chapter we deal with abelian integrals. They play a key role in the infinitesimal version of the 16th Hilbert problem. Recall that 16th Hilbert problem and its ramifications is one of the principal research subject of Christiane Rousseau and of the first author. We recall briefly the definition and explain the role of abelian integrals in 16th Hilbert problem. We also give a simple well-known proof of a property of abelian integrals. The reason for presenting it here is that it serves as a model for more complicated and more original treatment of abelian integrals in the study of Hamiltonian monodromy of fully integrable systems, which is the main subject of this chapter. We treat in particular the simplest example presenting non-trivial Hamiltonian monodromy: the spherical pendulum.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Business + Economics & Engineering + Technology"

Online-Abonnement

Springer Professional "Business + Economics & Engineering + Technology" gives you access to:

  • more than 102.000 books
  • more than 537 journals

from the following subject areas:

  • Automotive
  • Construction + Real Estate
  • Business IT + Informatics
  • Electrical Engineering + Electronics
  • Energy + Sustainability
  • Finance + Banking
  • Management + Leadership
  • Marketing + Sales
  • Mechanical Engineering + Materials
  • Insurance + Risk


Secure your knowledge advantage now!

inform now

Springer Professional "Engineering + Technology"

Online-Abonnement

Springer Professional "Engineering + Technology" gives you access to:

  • more than 67.000 books
  • more than 390 journals

from the following specialised fileds:

  • Automotive
  • Business IT + Informatics
  • Construction + Real Estate
  • Electrical Engineering + Electronics
  • Energy + Sustainability
  • Mechanical Engineering + Materials





 

Secure your knowledge advantage now!

inform now

Springer Professional "Business + Economics"

Online-Abonnement

Springer Professional "Business + Economics" gives you access to:

  • more than 67.000 books
  • more than 340 journals

from the following specialised fileds:

  • Construction + Real Estate
  • Business IT + Informatics
  • Finance + Banking
  • Management + Leadership
  • Marketing + Sales
  • Insurance + Risk



Secure your knowledge advantage now!

inform now
previous chapter Slow-Fast Dynamics and Its Application to a Biological Model
next chapter Towards a Science of Security Games
Literature
This content is only visible if you are logged in and have the appropriate permissions.
Metadata
Title
Abelian Integrals: From the Tangential 16th Hilbert Problem to the Spherical Pendulum
Authors
Pavao Mardešić
Dominique Sugny
Léo Van Damme
Copyright Year
2016
Book
Mathematical Sciences with Multidisciplinary Applications

Print ISBN: 978-3-319-31321-4

Electronic ISBN: 978-3-319-31323-8

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-31323-8_15

Premium Partners

    Image Credits