Introduction to modern dynamics. Chaos, networks, space and time (Q2929569)

The monograph consists of four parts and 11 chapters. Part 1. Geometric Mechanics.NEWLINENEWLINE1. Physics and geometry. 2. Hamiltonian dynamics and phase space. Part 2. Nonlinear dynamics. 3. Nonlinear dynamics and chaos. 4. Coupled oscillators and synchronization. 5. Network dynamics. Part 3. Complex systems. 6. Neurodynamics and neural networks. 7. Evolutionary dynamics. 8. Economic dynamics. Part 4. Relativity and space-time. 9. Metric spaces and geodesic motion. 10. Relativistic dynamics. 11. The general theory of relativity and gravitation.NEWLINENEWLINE The book combines the three main topics of modern dynamics which are generally out of the standard university programs, i.e. the chaos theory, the dynamics on complex networks and the general relativity. The author takes a geometric view of physics, concentrating on the time evolution of physical systems as the trajectories through abstract spaces. As a result, the abovementioned topics are described by a common and simple mathematical language through which any student can gain a unified physical intuition. Given the growing importance of complex dynamical systems in many areas of education, science and technology, the book provides students with an up-to-date foundation for their future careers.