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The parameterization method for one- dimensional invariant manifolds of higher dimensional parabolic fixed points

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  • We use the parameterization method to prove the existence and properties of one-dimensional submanifolds of the center manifold associated to the fixed point of $C^r$ maps with linear part equal to the identity. We also provide some numerical experiments to test the method in these cases.
    Mathematics Subject Classification: Primary: 37D10; Secondary: 37N05.

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