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- W2058352080 abstract "Abstract This work is concerned with the generic existence of homoclinic points for area preserving diffeomorphisms of compact orientable surfaces. We give a shorter proof of Pixton's theorem that shows that, C r -generically, an area preserving diffeomorphism of the two sphere has the property that every hyperbolic periodic point has transverse homoclinic points. Then, we extend Pixton's result to the torus and investigate certain generic aspects of the accumulation of the invariant manifolds all over themselves in the case of symplectic diffeomorphisms of compact manifolds." @default.
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- W2058352080 date "1987-12-01" @default.
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- W2058352080 title "On the generic existence of homoclinic points" @default.
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- W2058352080 doi "https://doi.org/10.1017/s0143385700004211" @default.
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