Gap phenomenon for some autonomous functionals.
On the global stable manifold
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 counter-example concerning a condition of Ogawa integrability
Infinite paths and cliques in random graphs
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.
Page 1