Index Theory for Symplectic Paths with Applications

This book gives an introduction to index theory for symplectic matrix paths and its iteration theory, as well as applications to periodic solution problems of nonlinear Hamiltonian systems. The applications of these concepts yield new approaches to some outstanding problems. Particular attention is given to the minimal period solution problem of Hamiltonian systems and the existence of infinitely many periodic points of the Poincaré map of Lagrangian systems on tori.

Researchers, graduate and postgraduate students from a wide range of areas inside mathematics or physics will benefit from this monograph. Teachers of advanced courses in symplectic geometry or Hamiltonian systems will also find it an excellent textbook.