Automorphisms of positive entropy on some hyperKähler manifolds via derived automorphisms of K3 surfaces

We construct examples of hyperKähler manifolds of Picard number two with automorphisms of positive entropy via derived automorphisms of K3 surfaces of Picard number one. Our hyperKähler manifolds are constructed as moduli spaces of Bridgeland stable objects in derived categories of K3 surfaces. Then automorphisms of positive entropy are induced by derived automorphisms of positive entropy on K3 surfaces.