Reduction of Morse Functions on Surfaces to Canonical Form by Smooth Deformation
1999, Volume 4, Number 3, pp. 53-60
Author(s):
Kudryavtseva E. A.
Relatively recently in works [3], [4] the topological classification of smooth Hamiltonian systems with one degree of freedom was obtained. When we study the stability of obtained topological invariants, the following natural question arised: is the space of all Morse functions with fixed number of minima and maxima on a closed surface connected? The present paper discusses this question and gives an algorithm of reduction of any Morse function on a closed orientable surface to the so-called canonical form.
Citation:
Kudryavtseva E. A., Reduction of Morse Functions on Surfaces to Canonical Form by Smooth Deformation, Regular and Chaotic Dynamics,
1999, Volume 4, Number 3,
pp. 53-60
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