Inverse Problems in Ordinary Differential Equations and Applications

  • Jaume Llibre
  • Rafael Ramírez

Part of the Progress in Mathematics book series (PM, volume 313)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Jaume Llibre, Rafael Ramírez
    Pages 1-40
  3. Jaume Llibre, Rafael Ramírez
    Pages 41-85
  4. Jaume Llibre, Rafael Ramírez
    Pages 87-116
  5. Jaume Llibre, Rafael Ramírez
    Pages 117-152
  6. Jaume Llibre, Rafael Ramírez
    Pages 153-163
  7. Jaume Llibre, Rafael Ramírez
    Pages 165-199
  8. Jaume Llibre, Rafael Ramírez
    Pages 201-251
  9. Back Matter
    Pages 253-266

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.


16th Hilbert problem Nambu bracket inverse problems ordinary differential equations planar polynomial differential systems vakonomic mechanics

Authors and affiliations

  • Jaume Llibre
    • 1
  • Rafael Ramírez
    • 2
  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBarcelonaSpain
  2. 2.Departament d'Enginyeria InformàticaUniversitat Rovira i VirgiliTarragona, CataloniaSpain

Bibliographic information