Text Reference |
I. Percival and D. Richards, Introduction to Dynamics, Cambridge University Press, 1982. Steven H. Strogatz, Nonlinear Dynamics and Chaos, Addison Weseley,1994. Edward Ott, Chaos in Dynamical Systems, Cambridge University Press,1993. E. A. Jackson, Perspectives of Nonlinear Dynamics, Vol. 1&2, Cambridge University Press, 1989. |

Description |
Physics of nonlinear systems, dynamical equations and constants of motion, phase space, fixed points, stability analysis, bifurcations and their classifications, Poincar`e section and iterative maps. One dimensional non--invertible maps, simple and strange attractors, period doubling and universality, intermittency, invariant measure, Lyapunov exponents. Higher dimensional systems, Henon map, Lorenz equations. Fractal geometry and examples of simple and fat fractals, concept of dimensions. Hamiltonian systems, integrability, Liouville`s theorem, action and angle variables, introduction to perturbation techniques, KAM theorem, area preserving maps, chaos and stochasticity. |