Dynamically exotic contact spheres in dimensions ≥ 7

Original · EN

We exhibit the first examples of contact structures on S²ⁿ⁻¹ with n≥ 4 and on S³× S², all equipped with their standard smooth structures, for which every Reeb flow has positive topological entropy. As a new technical tool for the study of the volume growth of Reeb flows we introduce the notion of algebraic growth of wrapped Floer homology. Its power stems from its stability under several geometric operations on Liouville domains.