Decimate 发表于 2025-3-23 11:52:04
Morse Theory,Morse theory’s object is the relation between the topological type of critical points of a function . and the topological structure of the manifold on which the function is defined.faucet 发表于 2025-3-23 14:26:07
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Applications of Morse Theory to Second Order Systems,system . and assume that 0 is a solution and that . (.. ≥ 0,0 ≤ . ≤ .) are the non-negative eigenvalues of .(0). The Liapunov theorem insures that if the geometric multiplicity of . is one and if ../.. ∉ N for ., then this system has a family of periodic solutions with minimal period tending to .. and with amplitude tending to 0.