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Progress in Mathematics

Inverse Problems in Ordinary Differential Equations and Applications

Authors: Llibre, Jaume, Ramírez, Rafael

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  • Solves the 16th Hilbert problem (restricted to algebraic limit cycles) based on generic assumptions
  • Presents a detailed analysis of transpositional relations, a generalization of the Hamiltonian principle
  • Features the Nambu bracket as central tool in the authors' approach on solving inverse problems in ODEs
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eBook 83,29 €
price for India (gross)
  • ISBN 978-3-319-26339-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
Hardcover 99,99 €
price for India (gross)
  • ISBN 978-3-319-26337-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover 99,99 €
price for India (gross)
  • ISBN 978-3-319-79935-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties. The Nambu bracket is the central tool in developing this approach. The authors start characterizing the ordinary differential equations in R^N which have a given set of partial integrals or first integrals. The results obtained are applied first to planar polynomial differential systems with a given set of such integrals, second to solve the 16th Hilbert problem restricted to generic algebraic limit cycles, third for solving the inverse problem for constrained Lagrangian and Hamiltonian mechanical systems, fourth for studying the integrability of a constrained rigid body. Finally the authors conclude with an analysis on nonholonomic mechanics, a generalization of the Hamiltonian principle, and the statement an solution of the inverse problem in vakonomic mechanics.

Reviews

“The book presents a new approach to … inverse problems, where the authors mainly use as an essential tool the Nambu bracket. They deduce new properties of this bracket, which plays a fundamental role in the proof of all the results and in their applications throughout the book. … The book is well written and contains new and valuable results in the development of the inverse problem in ordinary differential equations and its applications.” (Leonardo Colombo, Mathematical Reviews, January, 2017)


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook 83,29 €
price for India (gross)
  • ISBN 978-3-319-26339-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 99,99 €
price for India (gross)
  • ISBN 978-3-319-26337-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover 99,99 €
price for India (gross)
  • ISBN 978-3-319-79935-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Inverse Problems in Ordinary Differential Equations and Applications
Authors
Series Title
Progress in Mathematics
Series Volume
313
Copyright
2016
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-26339-7
DOI
10.1007/978-3-319-26339-7
Hardcover ISBN
978-3-319-26337-3
Softcover ISBN
978-3-319-79935-3
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XII, 266
Number of Illustrations
1 b/w illustrations, 8 illustrations in colour
Topics