The fundamantal part of the book deals with the investigation of the perturbable systems. Both autonomous and nonautonomous (periodic in time) systems are considered. The global analysis of systems close to the two-dimensional Hamiltonian ones takes a central place in the text. This global analysis includes the solution to problems such as the limit cycles, resonances, and nonregular dynamics. For the autonomous systems, one should note the analysis of the standard (Duffing and pendulum) equations including the solution to the "weakened" 16 Hilbert's problem, and for the nonautonomous systems one should note the mathematical foundations of the theory of synchronization of oscillations (the existence of new regimes, and the passage of invariant tori across the resonance zones under the change of detuning). The presentation is accompanied by examples.

Contents:

• Introduction and Review of Main Results
• Conservative Nonlinear Systems:
• Integrable Nonlinear Systems
• Non-Integrable Hamiltonian Systems
• Quasi-Conservative Nonlinear Systems:
• Perturbed Autonomous Systems with One Degree of Freedom
• Periodic Perturbations of Two-Dimensional Hamiltonian Systems
• Generalizations and Applications
• Non–Quasi-Integrable Systems

"The subject matter is well organized, each chapter building on the previous one."

"... the material is interesting and well presented, so this might be used as a textbook for a graduate course."