Time-Frequency Analysis of Nonlinear Dynamical Systems

Nonlinear dynamical systems are widely observed in many branches of physics ranging from Celestial Mechanics to Chemistry. In this book, we propose the method of Time-Frequency analysis based on wavelets to study the phase space structure of different nonlinear dynamical systems. We have investigated nonlinear dynamical systems from space dynamics and celestial mechanics. Also, the comparison with other methods such as Lyapunov Characteristic Exponents, Fourier Transform etc. is an important aspect. Different aspects of phase space structure such as resonance transition, stickiness, resonance trapping are explained using wavelet transform. The algorithm for the computation of Time-Frequency analysis based on wavelets is also explained in detail.