Synopses & Reviews
"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.
This heavily-illustrated book is the first ever to present discontinuous dynamical systems in time-varying domains where the corresponding switchability of a flow to the time-varying boundary in discontinuous dynamical systems is discussed.
Table of Contents
Chapter 1. Introduction.- Chapter 2. Flow Switchability.- Chapter 3. Transversal Motion and Sliding Phenomena.- Chapter 4. A Frictional Oscillator on Time-varying Belts.- Chapter 5. Two Systems with Impacts and Stick.- Chapter 6. Dynamical systems with Friction.- Chapter 7. Principles for System Interactions.