Introduction to Dynamical Systems - Lecture 1

Explore the fundamentals of dynamical systems in this comprehensive lecture by Soumitro Banerjee from the International Centre for Theoretical Sciences. Begin with discrete-time examples and ordinary differential equations, then progress to equilibrium points, linear ODEs, and eigenvalue calculations. Delve into nonlinear systems, examining attractors, limit cycles, and the Lorenz system. Investigate chaos theory and orbits on a torus before engaging in a Q&A session. Conclude by studying Poincaré sections, one-dimensional maps, fixed point stability, and various bifurcation types, including saddle-node and period-doubling bifurcations.