Preview
Unable to display preview. Download preview PDF.
References
V. I. Arnold, Proof of A. N. Kolmogorov's Theoren on the preservation of Quasi-Periodic Motions under small perturbations of the Hamiltonian, Russian Math. Surveys, 18, N. 5, 13–40 (1963).
V. I. Arnold, Small Divisor Problem in Classical and Celestial Mechanics, Russian Math. Surveys, 18, N.6, 85–191 (1963).
V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer Verlag, Graduate Text in Math. 1978.
S. Aubry. Theorey of the Devil's Staircase, Seminar on the Riemann Problem and complete integrability, 1978-79. Ed. D. G. Chudnovsky, Springer, Lecture Notes in Math., in press.
S. Aubry, P. Y. Le Daeron, G. Andre, Classical Ground-States of a one-dimensional Model for Incommensurate Structure, submitted to Comm. Math. Phys.
G. D. Birkhoff, On the Periodic Motions of Dynamical Systems, Acta Mathematica, 50, 359–379. Reprinted in Collected Mathematical Papers, vol. II, Amer, Math. Soc. N.Y, 333–353 (1950).
G. D. Birkhoff, Surface transformations and their dynamical applications, Acta Math., 43, 1–119 (1922) Reprinted in Collected Mathematical Papers, vol. II, Amer. Math. Soc. N.Y, 111–229 (1950).
G. D. Birkhoff, Sur Quelques, Courbes Fermeés Remarquable, Bull. Soc. Math. de France, 60, 1–26 (1932); Reprinted in Collected Mathematical Papers, Amer. Math. Soc., N.Y., 418–443 (1950).
A. Denjoy, Sur les courbes définies par les équations différentielles à la surface de tore, J. Math. Pure et Appliq, 11, 333–375 (1932).
J. M. Greene, The calculation of KAM surgaces, Ann. New York Acad. Sci., 357, 80–89 (1980).
M. R. Herman, Handwritten manuscript 1981
A. Katok, Some remarks on Birkhoff and Mather twist map theorems, Ergodic Theory and Dynamical Systems, 2, 2 (1982).
A. Katok, More about Birkhoff periodic orbits and Mather sets for twist maps, Preprint IRES, 1982.
A. Katok, Continuation of the preprint “More about Birkhoff periodic orbits and Mather sets for twist maps, 1982.
A. N. Kolmogorov, On Quasi Periodic Motions under small perturbations of the Hamiltonian, Doklady AN SSSR, 98, 4, 527–530 (1954) (in Russian).
J. N. Mather, Existence of quasi-periodic orbits for twist homeomorphism of the annulus, Topology, 1982.
J. N. Mather, A Criterion for non-existence of invariant circles. Preprint, 1982.
J. N. Mather. Glancing Billiards, Ergodic Theory and Dynamical Systems, 2, 3–4 (1982).
J. N. Mather, Non-existence of Invariant circles. Preprint, 1982.
J. N. Mather, Non-uniqueness of Solutions of Percival's Euler-Lagrange Equation. Preprint, 1982.
J. N. Mather, Concavity of the Lagrangian for Quasi-Periodic orbits, to appear in Comm. Math. Helv.
J. Moser, On Invariant Curves of Area-Preserving Mappings of an Annulus. Nach. Akad. Wiss. Gbttingen, Math.-Phys. Kl, IIa, N 1, 1–20 (1962).
J. Moser. Stable and Random Motions in Dynamical Systems, Princeton Univ. Press, 1973.
Z. Nitecki, Differentiable Dynamics, MIT Press, 1971.
I. C. Percival, Variational Principles for Invariant Tori and Cantori, in Symposium on Nonlinear Dynamics and Beam-Beam Interactions. Amer. Inst. of Phys. Conf. Proc. N. 57, ed. M. Month, J. C. Herrara, 302–310, 1980.
I. C. Percival, J. Phys. A: Math. Nucl. Gen 12, L57, 1979.
M. Rüssmann, Über invariante Kurven differenzierbarer Abbildungen eines Kreisringer, Nachr. Akad. Wiss. Göttingen, Math.-Phys. K1, II N 5, 67–105 (1970).
H. Rüssmann, On the existence of invariant curves of twist mappings of an annulus. Preprint, 1982. *** DIRECT SUPPORT *** A3418136 00002
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
Katok, A. (1983). Periodic and quasi-periodic orbits for twist maps. In: Garrido, L. (eds) Dynamical System and Chaos. Lecture Notes in Physics, vol 179. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12276-1_3
Download citation
DOI: https://doi.org/10.1007/3-540-12276-1_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12276-0
Online ISBN: 978-3-540-39594-2
eBook Packages: Springer Book Archive