Kopych M. Investigations of invariant submanifolds and their perturbations of the finite-dimensional reductions of completely intergrable Hamiltonian systems

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0401U001226

Thesis Registration Form

0401U001226.pdf

Applicant for

Specialization

  • 01.01.02 - Диференційні рівняння

26-04-2001

Specialized Academic Board

Д 26.001.37

Taras Shevchenko National University of Kyiv

Essay

The thesis is devoted to investigation of invariant submanifolds, their embeddings into the phase spaces, weakly and slowly perturbations of finite-dimensional reductions of completely integrable Hamiltonian systems. Embedding problem of integrable submnanifolds of Hamiltonian systems on the noncanonical symplectic cotangent manifolds is investigated, Poincare-Cartan's theory of transversal splitting of asymptotic Lagrangean manifolds for weakly and slowly perturbed Hamiltonian systems is developed.

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