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On the global stable manifold

Alberto Abbondandolo;  Pietro Majer — 2006

Studia Mathematica

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.

Infinite paths and cliques in random graphs

Alessandro Berarducci;  Pietro Majer;  Matteo Novaga — 2012

Fundamenta Mathematicae

We study the thresholds for the emergence of various properties in random subgraphs of (ℕ, <). In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the probability is made. The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.

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