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The Restricted Three-Body Problem and Holomorphic Curves

  • Urs Frauenfelder
  • Otto van Koert

Part of the Pathways in Mathematics book series (PATHMATH)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Urs Frauenfelder, Otto van Koert
    Pages 1-8
  3. Urs Frauenfelder, Otto van Koert
    Pages 9-28
  4. Urs Frauenfelder, Otto van Koert
    Pages 29-45
  5. Urs Frauenfelder, Otto van Koert
    Pages 47-56
  6. Urs Frauenfelder, Otto van Koert
    Pages 57-84
  7. Urs Frauenfelder, Otto van Koert
    Pages 85-92
  8. Urs Frauenfelder, Otto van Koert
    Pages 93-125
  9. Urs Frauenfelder, Otto van Koert
    Pages 127-162
  10. Urs Frauenfelder, Otto van Koert
    Pages 163-182
  11. Urs Frauenfelder, Otto van Koert
    Pages 183-206
  12. Urs Frauenfelder, Otto van Koert
    Pages 207-224
  13. Urs Frauenfelder, Otto van Koert
    Pages 225-241
  14. Urs Frauenfelder, Otto van Koert
    Pages 243-264
  15. Urs Frauenfelder, Otto van Koert
    Pages 265-284
  16. Urs Frauenfelder, Otto van Koert
    Pages 285-310
  17. Urs Frauenfelder, Otto van Koert
    Pages 311-321
  18. Urs Frauenfelder, Otto van Koert
    Pages 323-338
  19. Urs Frauenfelder, Otto van Koert
    Pages 339-356
  20. Back Matter
    Pages 357-374

About this book

Introduction

The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics.

The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves.  The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem.

Keywords

symplectic geometry contact geometry holomorphic curves celestial mechanics restricted three-body problem global surfaces of section symplectic dynamics

Authors and affiliations

  • Urs Frauenfelder
    • 1
  • Otto van Koert
    • 2
  1. 1.Mathematical InstituteUniversity AugsburgAugsburgGermany
  2. 2.Department of MathematicsSeoul National UniversityGwanak-guKorea (Republic of)

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-72278-8
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-72277-1
  • Online ISBN 978-3-319-72278-8
  • Series Print ISSN 2367-3451
  • Series Online ISSN 2367-346X
  • Buy this book on publisher's site
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