Perturbation Theory

G. Gaeta studied Theoretical Physics in Roma and New York; he had postdoctoral positions in Montreal, Paris, Madrid, and Utrecht and was Reader in Nonlinear Systems in Loughborough, UK, before landing in Milano, Italy, where he is now Professor of Mathematical Physics. His main fields of research are Mathematical Physics – in particular Nonlinear Systems, Perturbation Theory, and Symmetry – and Mathematical Biology. He is the author of over 150 research papers and 3 research monographs, together with a textbook in introductory Mathematical Biology. He is also the main organizer of the SPT (Symmetry and Perturbation Theory) series of conferences, which started in 1996, and the Director of the virtual Research Institute SMRI.

• Diagrammatic Methods in Classical Perturbation Theory.- Hamiltonian Perturbation Theory (and Transition to Chaos).- Kolmogorov-Arnold-Moser (KAM) Theory for Finite and Infinite Dimensional Systems.- n-Body Problem and Choreographies.- Nekhoroshev Theory.- Symmetry and Perturbation Theory in Non-linear Dynamics.- Normal Forms in Perturbation Theory.- Perturbation Analysis of Parametric Resonance.- Perturbation of Equilibria in the Mathematical Theory of Evolution.- Perturbation of Systems with Nilpotent Real Part.- Perturbation Theory.- Perturbation Theory in Celestial Mechanics.- Introduction to Perturbation Theory.- Perturbation Theory and Molecular Dynamics.- Perturbation Theory for Non-smooth Systems.- Perturbation Theory for PDEs.- Perturbation Theory in Quantum Mechanics.- Semiclassical Perturbation Theory.- Convergence of Perturbative Expansions.- Quantum Bifurcations.- Perturbation of superintegrable systems.- Computational methods in perturbation theory.- Perturbation theoryin general relativity and cosmology.- Perturbation Theory for Water Waves.- Perturbation Theory and the Method of Detuning.