Simon Allais

In 1992,Viterbo introduced new means to study the Hamiltonian dynamics of $\mathbb R^{2n}$ by applying Morse-theoretical methods to generating functions. Among his results, he gave a new proof of Gromov's non-squeezing theorem (1985) and sketched a proof of the more subtle symplectic camel theorem. A part of this work was generalized to the contact case by Sandon (2011) who provided a new way to derive the contact non-squeezing theorem of Eliashberg, Kim and Polterovich (2006). We will recall the main points of this theory and show how it allows us to derive a proof of the symplectic camel theorem which can easily be extended to the compact case.