Discontinuous Dynamical Systems on Time varying Domains Discontinuous Dynamical Systems on Time varying Domains is the first monograph focusing on this topic. While in the classic theory of dynamical systems the focus is on dynamical systems on time invariant domains this book presents discontinuous dynamical systems on time varying domains where the corresponding switchability of a flow to the time varying boundary in discontinuous dynamical systems is discussed. From such a theory principles of dynamical system interactions without any physical connections are presented. Several discontinuous systems on time varying domains are analyzed in detail to show how to apply the theory to practical problems. The book can serve as a reference book for researchers advanced undergraduate and graduate students in mathematics physics and mechanics. Dr. Albert C. J. Luo is a professor at Southern Illinois University Edwardsville USA. His research is involved in the nonlinear theory of dynamical systems. His main contributions are in the following aspects: a stochastic and resonant layer theory in nonlinear Hamiltonian systems singularity on discontinuous dynamical systems and approximate nonlinear theories for a deformable body.