Perturbation Theory

This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare'-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.

Title is also available as part of a set: Perturbation Theory (978-1-0716-2622-1)

Auteur
Giuseppe Gaeta is currently Professor of Mathematical Physics at the Università degli Studi di Milano, Milan, Italy, and Director of SMRI, Italy. Professor Gaeta studied Physics in Rome and subsequently held research or teaching positions in CRM, Montreal (Canada); IHES, Bures-sur-Yvette (France); École Polytechnique, Palaiseau (France); Rijksuniversiteit, Utrecht (the Netherlands); Universidad Carlos III and Universidad Complutense, Madrid (Spain); and Loughborough University (UK). He is the author of over 150 scientific research papers and three research monographs (one in collaboration with G. Cicogna and one w3ith M.A. Rodriguez). His main scientific interests are the roles of Symmetry in physical theories and in nonlinear dynamics.

Contenu
Diagrammatic Methods in Classical Perturbation TheoryHamiltonian Perturbation Theory (and Transition to Chaos)Kolmogorov-Arnold-Moser (KAM) Theory for Finite and Infinite Dimensional Systemsn-Body Problem and ChoreographiesNekhoroshev TheorySymmetry and Perturbation Theory in Non-linear DynamicsNormal Forms in Perturbation TheoryPerturbation Analysis of Parametric ResonancePerturbation of Equilibria in the Mathematical Theory of EvolutionPerturbation of Systems with Nilpotent Real PartPerturbation TheoryPerturbation Theory in Celestial MechanicsIntroduction to Perturbation TheoryPerturbation Theory and Molecular DynamicsPerturbation Theory for Non-smooth SystemsPerturbation Theory for PDEsPerturbation Theory in Quantum MechanicsSemiclassical Perturbation TheoryConvergence of Perturbative ExpansionsQuantum BifurcationsPerturbation of superintegrable systemsComputational methods in perturbation theoryPerturbation Theory for Water Waves
Perturbation Theory and the Method of DetuningPeriodic Rogue Waves and Perturbation TheoryConvergent perturbative expansion in Condensed Matter and Quantum Field TheoryQuantum Adiabatic TheoremExact and perturbation methods in the dynamics of legged locomotionCorrelation corrections as a perturbation to the quasi-free approximation in many-body quantum systems