On the autonomous metric on the group of area-preserving diffeomorphisms of the 2-disc

الأصل · EN

Let D² be the open unit disc in the Euclidean plane and let G:= Diff(D2; area) be the group of smooth compactly supported area-preserving diffeomorphisms of D². We investigate the properties of G endowed with the autonomous metric. In particular, we construct a bi-Lipschitz homomorphism Zᵏ → G of a finitely generated free abelian group of an arbitrary rank. We also show that the space of homogeneous quasi-morphisms vanishing on all autonomous diffeomorphisms in the above group is infinite dimensional.