We introduce the concept of k-(semi)-dilation for Liouville domains, which is a generalization of symplectic dilation defined by Seidel-Solomon. We prove that the existence of k-(semi)-dilation is a property independent of certain fillings for asymptotically dynamically convex (ADC) manifolds. We construct examples with k-dilations, but not k−1-dilations for all k⩾0. We extract invariants taking value in N∪{∞} for Liouville domains and ADC contact manifolds, which are called the order of (semi)-dilation. The order of (semi)-dilation serves as embedding and cobordism obstructions. We determine the order of (semi)-dilation for many Brieskorn varieties and use them to study cobordisms between Brieskorn manifolds.