Kadubovsky O. Vector fields and Lyapunov functions on surfaces

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0406U005142

Thesis Registration Form

0406U005142.pdf

Applicant for

Specialization

  • 01.01.02 - Диференційні рівняння

19-12-2006

Specialized Academic Board

Д 26.206.02

The Institute of Mathematics of NASU

Essay

We obtained a new topological classifications of polar Morse-Smale vector fields on smooth closed surfaces and calculated the number of such fields on oriented surfaces of genus 3. We give a necessary and sufficient condition of topological equivalence of smooth vector fields which have only one saddle point. We also calculated the number of non equivalent such fields with one source and one sink on surfaces of genus g>1. Also the existence of the transitive flows with fixed set of singularities on closed oriented surfaces of genus g>1 is proved.

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Files

Dis.pdf

aref.doc

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