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What is the difference between the theory of Morse study in the book of Milnor: "Morse theory "and that studied in the book" ciritical point theory and Hamiltonian systems "

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This is the same theory but in the book " ciritical point theory and Hamiltonian systems " authors show applications of Morse theory to Hamiltonian systems. In particular using Morse inequalities you say something about minimal number of critical points on a given manifolds (at least as many as sum of Betti numbers).

For a general paper about Morse theory I highly recommend R.Bott - Morse theory indomitable Publications Mathématiques de l'IHÉS, 68 (1988), p. 99-114

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so to see Morse theory in Hilber space i must study the Morse inequality ,right ? –  Vrouvrou Jun 3 '13 at 11:05
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