Introduction to Modern Dynamics: Chaos, Networks, Space, and Time

This book translates important topics of advanced classical physics, usually the rarefied domain of physics graduate classes, into simple language accessible to undergraduate students majoring in the physical sciences and engineering. It presents a unifying approach to the physics of chaos, nonlinear systems, dynamic networks, evolutionary dynamics, econophysics and the theory of relativity. All of these topics share a common foundation in which complex dynamics are represented as simple trajectories within a geometric space. This approach is called geometric mechanics, and advanced concepts in general relativity or network theory become straightforward explorations of geometric curves. Each chapter has many worked examples and simple computer simulations that allow the student to explore the rich phenomena of nonlinear physics.