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Critical Point Theory for Lagrangian Systems

Marco Mazzucchelli (Autor)

Buch | Hardcover

XII, 188 Seiten

2011 | 2012
Springer Basel (Verlag)
978-3-0348-0162-1 (ISBN)

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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 investigateexistence 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.

1 Lagrangian and Hamiltonian systems.- 2 Functional setting for the Lagrangian action.- 3 Discretizations.- 4 Local homology and Hilbert subspaces.- 5 Periodic orbits of Tonelli Lagrangian systems.- A An overview of Morse theory.-Bibliography.- List of symbols.- Index.

From the reviews:

"This monograph concerns the use of critical point theory tools in connection with questions of existence and multiplicity of periodic solutions of Lagrangian systems. ... The monograph contains several proofs and seems to be especially suitable for researchers and advanced graduate students interested in applications of critical point theory to boundary value problems for Lagrangian systems." (Maria Letizia Bertotti, Mathematical Reviews, September, 2013)

"The results of critical point theory provide powerful techniques to investigate and study aspects of Lagrangian systems such as existence, multiplicity or uniqueness of solutions of the Euler-Lagrange equations with prescribed boundary conditions. ... A bibliography with 88 entries, a list of symbols distributed on each chapter, and a subject index complete the work. The book is self-contained and rigorously presented. Various aspects of it should be of interest to graduate students and researchers in this dynamic field of mathematics." (Dorin Andrica, Zentralblatt MATH, Vol. 1246, 2012)

Erscheint lt. Verlag	11.11.2011
Reihe/Serie	Progress in Mathematics
Zusatzinfo	XII, 188 p.
Verlagsort	Basel
Sprache	englisch
Maße	155 x 235 mm
Gewicht	436 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Euler-Lagrange equations • Lagrange-Analysis • Lagrangian dynamics • Morse Theory • periodic orbits
ISBN-10	3-0348-0162-9 / 3034801629
ISBN-13	978-3-0348-0162-1 / 9783034801621
Zustand	Neuware