Blow-up solutions of autonomous ordinary differentialequations (ODEs) which are unstable under perturbations of initial conditions are studied . They are obtained as trajectories on stable manifolds of hyperbolic (saddle) equilibria atinfinity . In this process, important features are obtained: smooth dependenceof blow-up times on initial points near blow-ups, level set distribution ofblow-upsolutions, singular behavior of blow- upsolutions, organization of the phase space via separatrices (stable manifolds) In particular, we show that unstable blow up solutions themselves canseparate initial conditions into two regions where solution trajectories are globally bounded or blow up, no matter how large initial points are

Author(s) : Jean-Philippe Lessard, Kaname Matsue, Akitoshi Takayasu

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Keywords : blow - initial - solutions - unstable - points -

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