Abstract:  'We deal with the question under which conditions a given Hamiltonian diffeomorphism on an even-dimensional ball D²ⁿ embeds into the Reeb flow of a contact form on the odd-dimensional sphere S²ⁿ⁺¹ and give a general sufficient criterion for arbitrary dimensions. A crucial ingredient is Lerman’s cut construction. In the special case n =1, we consider irrational pseudorotations on D² constructed by Fayad and Katok and see that they embed into the Reeb flow of a dynamically convex contact form on S³.'