E. A. KUDRYAVTSEVA FacultyofMechanics and Mathematics Department of Di erential Geometry and Applications Moscow State University Vorob'ievy gory, 119899 Moscow, Russia E-mail: ekudr@beta.math.msu.su REDUCTION OF MORSE FUNCTIONS ON SURFACES TO CANONICAL FORM BY SMOOTH DEFORMATION Received September 12, 1999 , Relatively recently in works 3, 4 the topological classi cation of smooth Hamiltonian systems with one degree of freedom was obtained. ... The Reeb graph of a function is de ned as follows. ...

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