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Lagrangian systems constitute a very important and old class in dynamics. Their origin dates back to the end of the eighteenth century, with Joseph-Louis Lagrange’s reformulation of classical mechanics. The main feature of Lagrangian dynamics is its variational flavor: orbits are extremal points of an action functional. The development of critical point theory in the twentieth century provided a powerful machinery to investigate existence and multiplicity questions for orbits of Lagrangian systems. This monograph gives a modern account of the application of critical point theory, and more specifically Morse theory, to Lagrangian dynamics, with particular emphasis toward existence and multiplicity of periodic orbits of non-autonomous and time-periodic systems.

Critical point theory (Mathematical analysis). --- Lagrangian functions. --- Critical point theory (Mathematical analysis) --- Lagrangian functions --- Mathematics --- Engineering & Applied Sciences --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Operations Research --- Geometry --- Applied Physics --- Dynamics. --- Calculus of variations. --- Isoperimetrical problems --- Variations, Calculus of --- Dynamical systems --- Kinetics --- Functions, Lagrangian --- Mathematics. --- Ergodic theory. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Mathematical physics. --- Mathematical Physics. --- Dynamical Systems and Ergodic Theory. --- Global Analysis and Analysis on Manifolds. --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Maxima and minima --- Calculus of variations --- Dynamics --- Mathematical optimization --- Differential topology --- Global analysis (Mathematics) --- Differentiable dynamical systems. --- Global analysis. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Topological dynamics --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Functions of complex variables --- Geometry, Algebraic --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Physical mathematics