Prykarpats'kyj Y. Symplectic analysis of integral manifolds of the completely integrable Hamiltonian systems and its adiabatic perturbations

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0499U001482

Thesis Registration Form

0499U001482.pdf

Applicant for

Specialization

  • 01.01.02 - Диференційні рівняння

15-06-1999

Specialized Academic Board

Д 26.206.02

The Institute of Mathematics of NASU

Essay

We suggest an analitical approach to construct in the explicit form the embedding mapping of the invariant manifolds of completely integrable via Liuville algebraic-polinomial dynamical systems . Based on this approach the existence of the adiabatic invariants for a slowly perturbed dynamical system is investigated. The parallel transfering equastion for the connection for the Burgers dynamical system was found and explicit form of the associated Lax-type representation was built.

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