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Index Theory for Symplectic Paths with Applications (Hardcover, 2002 ed.)
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Index Theory for Symplectic Paths with Applications (Hardcover, 2002 ed.)
Series: Progress in Mathematics, 207
Expected to ship within 10 - 15 working days
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This book is based upon my monograph Index Theory for Hamiltonian
Systems with Applications published in 1993 in Chinese, and my
notes for lectures and courses given at Nankai University, Brigham
Young University, ICTP-Trieste, and the Institute of Mathematics of
Academia Sinica during the last ten years. The aim of this book is
twofold: (1) to give an introduction to the index theory for
symplectic matrix paths and its iteration theory, which form a
basis for the Morse theoretical study on Hamilto nian systems, and
to give applications of this theory to periodic boundary value
problems of nonlinear Hamiltonian systems. Here the iteration
theory means the index theory of iterations of periodic solutions
and symplectic matrix paths. (2) to serve as a reference book on
these topics. There are many different ways to introduce the index
theory for symplectic paths in order to establish Morse type index
theory of Hamiltonian systems. In this book, I have chosen a
relatively elementary way, i.e., the homotopy classification method
of symplectic matrix paths. It depends only on linear algebra,
point set topology, and certain basic parts of linear functional
analysis. I have tried to make this part of the book self-contained
and at the same time include all of the major results on these
topics so that researchers and students interested in them can read
it without substantial difficulties, and can learn the main results
in this area for their possible applications."
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