Symplectic Twist Maps (World Scientific (2001)) is a graduate textbook/research monograph on Symplectic Twist Maps and their relationship to Hamiltonian and Lagrangian systems. Theorems on existence of periodic orbits of Symplectic Twist Maps and Hamiltonian systems are central to the book. One of the goals of the book is to promote finite dimensional methods in the variational calculus approach to Hamiltonian systems. The techniques involve Conley-Morse Theory, which is reviewed in an appendix. These techniques give rise to the concept of ghost tori which are of particular interest in the dimension 2 case (ghost circles). Themes explored also include the open problem of finding orbits of all (in particular irrational) rotation vectors and the relationship between the theory of twist maps and symplectic topology.

You can download the introduction and detailed contents, both in pdf format. You can also read the Math Review about this book (MR1992005 (2004f:37070) - you will need a password to get in). Some reference typos slipped through the book. You can check the Erratum.

• Twist Maps of the Annulus
• The Aubry-Mather Theorem
• Ghost Circles
• Symplectic Twist Maps
• Periodic Orbits for Symplectic Twist Maps of Tn x IRn
• Invariant Manifolds
• Hamiltonian Systems vs. Twist Maps
• Periodic Orbits for Hamiltonian Systems
• Generalizations of the Aubry-Mather Theorem
• Appendix on Symplectic Geometry
• Appendix on Morse and Conley Index Theory

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