Proof of the Main Theorem

  • Vladimir F. Lazutkin
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 24)


This chapter contains the detailed proof of Theorem 11.6. First, we prove the continuous-time version of the Theorem (§§18–27) and then, in §28, we deduce the discrete-time theorem. In §18 we show that one may set γ = 1, and pass to a suitable formulation in angle-frequency variables. Some technical devices are exposed in §19. The description of an iterative process which yields the desired objects is placed in §20. Other sections (§§21–26) contain routines checking the inequalities necessary for the iterative process to occur correctly and their simple consequences. In §27 we summarize the results and establish that the objects obtained satisfy the conditions of the conclusion of Theorem 11.6.


Discrete Time Iterative Process Continuous Time Symplectic Structure Hamiltonian Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Vladimir F. Lazutkin
    • 1
  1. 1.Department of Mathematical Physics Institute of PhysicsSt. Petersburg State UniversityPetrodvorets St. PetersburgRussia

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