Convexity Methods In Hamiltonian Mechanics

I. Linear Hamiltonian Systems.- 1. Floquet Theory and Stability.- 2. Krein Theory and Strong Stability.- 3. Time-Dependence of the Eigenvalues of R (t).- 4. Index Theory for Positive Definite Systems.- 5. The Iteration Formula.- 6. The Index of a Periodic Solution to a Nonlinear Hamiltonian System.- 7. Examples.- 8. Non-periodic Solutions: The Mean Index.- II. Convex Hamiltonian Systems.- 1. Fundamentals of Convex Analysis.- 2. Convex Analysis on Banach Spaces.- 3. Integral Functionals on L?.- 4. The Clarke Duality Formula.- III. Fixed-Period Problems: The Sublinear Case.- 1. Subquadratic Hamiltonians.- 2. An Existence Result.- 3. Autonomous Systems.- 4. Nonautonomous Systems.- 5. Other Problems.- IV. Fixed-Period Problems: The Superlinear Case.- 1. Mountain-Pass Points.- 2. A Preliminary Existence Result.- 3. The Index at Mountain-Pass Points.- 4. Subharmonics.- 5. Autonomous Problems and Potential Wells.- V. Fixed-Energy Problems.- 1. Existence, Length, Stability.- 2. Multiplicity in the Pinched Case.- 3. Multiplicity in the General Case.- 4. Open Problems.