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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."
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.
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