Geography of Order and Chaos in Mechanics

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Focusing on quasi-integrable Hamiltonian systems, this monograph delves into the subtle dynamics of integrable systems affected by perturbations. It employs both analytic and numerical methods to investigate notable examples like the hydrogen atom and the solar system, utilizing advanced techniques such as frequency-modified Fourier transforms and wavelets. The work also references foundational concepts from KAM and Nekhoroshev theorems, providing a comprehensive understanding of the systems' behavior and stability.