References
- Poincaré H. Mémoire sur les courbes définies par une équation différentielle. J Math Pures Appl IV Sér. 1885;1:167–244.
- Denjoy A. Sur les courbes définies ls équations différentielle á la surface du tore. J Math Pures Appl. 1932;11(9):333–375.
- Bolyai PG. Selected works. Izd-vo Latv Akad Nauk, Riga; 1961.
- Arnold VI. Small divisors. I. On the mapping of a circle into itself. Izv Akad Nauk SSSR, Ser Mat. 1961;25(1):21–86.
- Mitropoliskii JuA, Samoilenko AM. The structure of trajectories on a toroidal manifold. Dokl Akad Nauk USSR. 1964;8:984–985.
- Samoilenko AM. The problem of the perturbation theory of trajectories on the torus. Ukr Mat Zh. 1964;16(6):769–782.
- Moser J. A rapidly convergent iteration method and nonlinear differential equations, II. Ann Scoula Norm Sup Pisa. 1966;20(3):499–536.
- Herman M. Sur la conjugaison differentiable des diffeomorphismes du cercle a des rotations. Inst Hautes Etudes Sci Publ Math. 1979;49:5–233.
- Moser J. Convergent series expansions for quasi-periodic motions. Math Ann. 1967;169:136–176.
- Pöschel J. KAM á la R. Regul Chaotic Dyn. 2011;16:17–23.
- Rüssmann H. KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character. Discrete Contin Dyn Syst Ser S. 2010;3:683–718.
- Chavaudret C, Marmi S. Reducibility of quasiperiodic cocycles under a Brjuno–Rüssmann arithmetical condition. J Mod Dyn. 2012;6:59–78.
- Zhang D, Xu J. On invariant tori of vector field under weaker non-degeneracy condition. Nonlinear Differ Equ Appl. 2015;22:1381–1394.
- Dinaburg EI, Sinai YaG. The one-dimensional Schrödinger equation with quasiperiodic potential. Funk Anal Appl. 1975;9:279–289.
- Rüssmann H. On the one-dimensional Schrödinger equation with a quasiperiodic potential. In: Nonlinear dynamics (International Conference, NewYork, 1979); New York: The New York Academy of Sciences. 1980. (Annals of the New York Academy of Sciences; 357).
- Eliasson LH. Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation. Commun Math Phys. 1992;146(3):447–482.
- Johnson R, Moser J. The rotation number for almost periodic potentials. Commun Math Phys. 1982;84(3):403–438.
- Sorets E, Spencer T. Positive Lyapunov exponents for Schrödinger operators with quasi-periodic potentials. Commun Math Phys. 1991;142(3):543–566.
- Moser J, Pöschel J. An extension of a result by Dinaburg and Sinai on quasiperiodic potentials. Comment Math Helv. 1984;59(1):39–85.
- Broer H, Puig J, Simó C. Resonance tongues and instability pockets in the quasi-periodic Hill-Schrödinger equation. Commun Math Phys. 2003;241(2–3):467–503.
- Broer H, Simó C. Hill’s equation with quasi-periodic forcing: resonance tongues, instability pockets and global phenomena. Bol Soc Bras Mat. 1998;29(2):253–293.
- Gentile G, Cortez DA, Barata JCA. Stability for quasi-periodically perturbed Hill’s equations. Commun Math Phys. 2005;260:403–443.
- Louis N. Topics in nonlinear functional analysis. Courant lecture notes in mathematics, Vol. 6. New York University, Curant Institute of Mathematical Sciences, New York; Providence (RI): American Mathematical Society; 2001.
- Gallavotti G. Classical mechanics and renormalization group, Lectures notes, 1983 Erice summer school, Ed. A. Wightman, G. Velo: NY:Plenum; 1985.
- Xu J, You J, Qiu Q. Invariant tori of nearly integrable Hamiltonian susyem with degeneracy. Math Z. 1997;226:375–386.