Perturbation Methods for Hamiltonian Systems. Generalizations

  • Georgio Eugenio Oscare Giacaglia
Part of the Applied Mathematical Sciences book series (AMS, volume 8)


This chapter is devoted to two main goals. First introduce the reader to known methods of canonical perturbations, describe them in a heuristic way and give examples so as to motivate the theorems presented in Chapters III and IV. Second, present some basic results about iterative procedures of fundamental importance on methods of averaging. Major contributors to this area are Lindstedt (1884), Poincaré (1893), Whittaker (1916), Siegel (1941), Krylov (1947), Bogoliubov (1945), Kolmogorov (1953), Arnol’d (1963), Diliberto (1961), Pliss (1966), Kyner (1961), Moser (1962), Hale (1961) with several overlappings in results. Many of these results have been unified and consolidated in celebrated books by Siegel (1956), Wintner (1947), Newytskii-Stepanov (1960), Cesari (1963), Hale (1969), Abraham (1967), Birkhoff (1927), Bogoliubov-Mitropolskii (1961), Lefschetz (1959), Minorsky (1962), Sansone-Conti (1964), Sternberg (1970).


Power Series Hamiltonian System Average Method Canonical Transformation Celestial Mechanics 
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Copyright information

© Springer-Verlag New York Inc. 1972

Authors and Affiliations

  • Georgio Eugenio Oscare Giacaglia
    • 1
    • 2
  1. 1.University of Sao PauloBrazil
  2. 2.University of Texas at AustinUSA

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