Displaying similar documents to “The role of center manifolds in ordinary differential equations”

On the global stable manifold

Alberto Abbondandolo, Pietro Majer (2006)

Studia Mathematica

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We give an alternative proof of the stable manifold theorem as an application of the (right and left) inverse mapping theorem on a space of sequences. We investigate the diffeomorphism class of the global stable manifold, a problem which in the general Banach setting gives rise to subtle questions about the possibility of extending germs of diffeomorphisms.

A homological selection theorem implying a division theorem for Q-manifolds

Taras Banakh, Robert Cauty (2007)

Banach Center Publications

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We prove that a space M with Disjoint Disk Property is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. This implies that the product M × I² of a space M with the disk is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. The proof of these theorems exploits the homological characterization of Q-manifolds due to Daverman and Walsh, combined with the existence of G-stable points in C-spaces. To establish the existence of such points we prove (and...