KAM Theory for Lower-Dimensional Tori

chapter 1  hamiltonian mechanics  1.1  the basic concepts of dynamical system  1.2  differential formchapter 2  hamiltonian system  2.1  classical hamiltonian and generalized hamiltonian  2.2  completely integrable systems and nearly integrable systemschapter 3  kam theorem  3.1  the classical kam theorem  3.2  lower-dimensional kam theorem  3.3  the generalized kam theoremchapter 4  lower-dimensional invariant tori in hamiltonian svstem  4.1  introduction  4.2  kam step  4.3  iteration lemma  4.4  proof of the main result  4.5  examplechapter 5  kam-type theorem with a quasi-periodic perturbation  5.1  introduction  5.2  the kam step  5.3  iteration lemma  5.4  proof of the main result  5.5  some exampleschapter 6  the persistence of lower-dimensional tori for generalized hamiltonian  6.1  introduction and main result  6.2  kam step  6.3  iteration lemma  6.4  proof of the main resultchapter 7  hyperbolic invariant tori for generalized hamiltonian systems  7.1  introduction and main result  7.2  kam step  7.3  iteration lemma  7.4  proof of the main result  7.5  exampleschapter 8 the hyperbolic invariant tori of the symplectic mappings  8.1  introduction  8.2  outline of the proof of theorem 8.1.1  8.3  estimates in one step  8.4  iteration lemma  8.5  proof of the main resultchapter 9  appendix  9.1  some facts about analytic functions  9.2  technical lemmabibliography