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New & Forthcoming Titles | Critical Point Theory for Lagrangian Systems

Critical Point Theory for Lagrangian Systems

Series: Progress in Mathematics, Vol. 293

Mazzucchelli, Marco

2012, XII, 188 p.

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  • Collects, in a rigorous and consistent style, many important results that are sparse in the literature
  • Exposition is self-contained
  • Arguments are presented in an elementary way in order to be accessible to the non-specialists

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.

Content Level » Research

Keywords » Euler-Lagrange equations - Lagrangian dynamics - Morse theory - periodic orbits

Related subjects » Birkhäuser Mathematics

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