Bibliografia de SISTEMES HAMILTONIANS - MA1

Bibliografia de SISTEMES HAMILTONIANS [AKN06]

V.I. Arnol0 d, V.V. Kozlov, and A.I. Neishtadt. Dynamical Systems III: Mathematical aspects of classical and celestial mechanics, volume 3 of Encyclopaedia Math. Sci. Springer-Verlag, Berlin–Heidelberg, 3rd edition, 2006.

[AM78]

R. Abraham and J.E. Marsden. Foundations of mechanics. Benjamin/Cummings, Reading, Mass., 2nd edition, 1978.

[AM87]

M. Adler and P. van Moerbeke. A systematic approach towards solving integrable systems. Academic Press, New York, 1987.

[Arn80]

V.I. Arnol0 d. Chapitres suppl´ementaires de la th´eorie des ´equations diff´erentielles ordinaires. Mir, Moscou, 1980. – En angl`es: Geometrical methods in the theory of ordinary differential equations, Springer-Verlag, New York, 2a edici´ o, 1988.

[Arn89]

V.I. Arnol0 d. Mathematical methods of classical mechanics, volume 60 of Grad. Texts in Math. SpringerVerlag, New York, 2nd edition, 1989. – En franc`es: Les m´ethodes math´ematiques de la m´ecanique classique, Mir, Moscou, 1976.

[Arn94]

V.I. Arnol0 d. Ecuaciones diferenciales ordinarias. Rubi˜ nos-1860, Madrid, 1994. ´ – En franc`es: Equations diff´erentielles ordinaires, Mir, Moscou, 1974.

[BHS96]

H.W. Broer, G.B. Huitema, and M.B. Sevryuk. Quasi-periodic motions in families of dynamical systems: order amidst chaos, volume 1645 of Lect. Notes in Math. Springer-Verlag, Berlin–Heidelberg, 1996.

[Bir27]

G.D. Birkhoff. Dynamical systems. Amer. Math. Soc., New York, 1927.

[Bou55]

E. Bour. Sur l’int´egration des ´equations diff´erentielles de la m´ecanique analytique. J. Math. Pures Appl., 20:185–200, 1855. J. Liouville, Note ` a l’occasion du m´emoire pr´ec´edent, J. Math. Pures Appl., 20:201–202, 1855.

[Car72]

H. Cartan. Formas diferenciales. Omega, Barcelona, 1972.

[Car81]

J. Carr. Applications of centre manifold theory, volume 35 of Appl. Math. Sci. Springer-Verlag, New York, 1981.

[CH82]

S.-N. Chow and J.K. Hale. Methods of bifurcation theory, volume 251 of Grundlehren Math. Wiss. SpringerVerlag, New York, 1982.

[CL55]

E.A. Coddington and N. Levinson. Theory of ordinary differential equations. McGraw-Hill, New York– Toronto–London, 1955.

[Cus78]

R. Cushman. Examples of nonintegrable analytic Hamiltonian vector fields with no small divisors. Trans. Amer. Math. Soc., 238:45–55, 1978.

[DG96]

A. Delshams and P. Guti´errez. Estimates on invariant tori near an elliptic equilibrium point of a Hamiltonian system. J. Differential Equations, 131(2):277–303, 1996.

[Eis61]

L.P. Eisenhart. Continuous groups of transformations. Dover, New York, 1961.

[Gan75]

F. Gantmacher. Lectures in analytical mechanics. Mir, Moscow, 1975.

[GDF+ 89] A. Giorgilli, A. Delshams, E. Fontich, L. Galgani, and C. Sim´o. Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem. J. Differential Equations, 77:167–198, 1989. [Gia72]

G.E.O. Giacaglia. Perturbation methods in non-linear systems, volume 8 of Appl. Math. Sci. SpringerVerlag, New York, 1972.

[Gio03]

A. Giorgilli. Exponential stability of Hamiltonian systems. In Dynamical systems. Part I, Pubbl. Cent. Ric. Mat. Ennio Giorgi, pages 87–198. Scuola Norm. Sup., Pisa, 2003.

[Gol94]

H. Goldstein. Mec´ anica cl´ asica. Revert´e, Barcelona, 2nd edition, 1994.

[Gol01]

C. Gol´e. Symplectic twist maps: global variational techniques, volume 18 of Adv. Ser. Nonlinear Dynam. World Scientific, Singapore, 2001.

[HPS77]

M.W. Hirsch, C.C. Pugh, and M. Shub. Invariant manifolds, volume 583 of Lect. Notes in Math. SpringerVerlag, Berlin, 1977.

[Jor99]

` Jorba. A methodology for the numerical computation of normal forms, centre manifolds and first A. integrals of Hamiltonian systems. Experiment. Math., 8(2):155–195, 1999.

[Kel67]

A. Kelley. The stable, center-stable, center, center-unstable, unstable manifolds. J. Differential Equations, 3:546–570, 1967.

[KH95]

A. Katok and B. Hasselblatt. Introduction to the modern theory of dynamical systems, volume 54 of Encyclopedia of Math. Appl. Cambridge Univ. Press, 1995.

[Laz93]

V.F. Lazutkin. KAM theory and semiclassical aproximations to eigenfunctions, volume 24 of Ergeb. Math. Grenzgeb. (3). Springer-Verlag, Berlin–Heidelberg, 1993.

[LL75]

L.D. Landau and E.M. Lifshitz. Mec´ anica, volume 1 of Curso de F´ısica Te´ orica. Revert´e, Barcelona, 1975.

[Lla01]

R. de la Llave. A tutorial on KAM theory. In A. Katok, R. de la Llave, Ya. Pesin, and H. Weiss, editors, Smooth ergodic theory and its applications (Seattle, WA, 1999), volume 69 of Proc. Sympos. Pure Math., pages 175–292. AMS, Providence, RI, 2001. (versi´o revisada: ftp://ftp.ma.utexas.edu/pub/papers/ llave/tutorial.pdf , 2004).

[LM88]

P. Lochak and C. Meunier. Multiphase averaging for classical systems, with applications to adiabatic theorems, volume 72 of Appl. Math. Sci. Springer-Verlag, New York, 1988.

[LMS99]

J. Llibre, K.R. Meyer, and J. Soler. Bridges between the generalized Sitnikov family and the Lyapunov family of periodic orbits. J. Differential Equations, 154(1):140–156, 1999. – Erratum: J. Differential Equations, 169(2):654, 2001.

[MH92]

K.R. Meyer and G.R. Hall. Introduction to Hamiltonian dynamical systems and the N -body problem, volume 90 of Appl. Math. Sci. Springer-Verlag, New York, 1992.

[Mos58]

J. Moser. New aspects in the theory of stability of Hamiltonian systems. Comm. Pure Appl. Math., 11:81–114, 1958.

[Mos68]

J. Moser. Lectures on Hamiltonian systems. Mem. Amer. Math. Soc., 81:1–60, 1968. AMS, Providence, RI.

[MR94]

J.E. Marsden and T.S. Ratiu. Introduction to mechanics and symmetry, volume 17 of Texts Appl. Math. Springer-Verlag, New York, 1994.

[Pol76]

H. Pollard. Celestial mechanics, volume 18 of Carus Math. Monogr. Math. Assoc. America, 1976.

[Sim89]

C. Sim´ o. Estabilitat de sistemes hamiltonians. Mem. Reial Acad. Ci`enc. Arts Barcelona, 48(7):305–336, 1989.

[Sim90]

C. Sim´ o. On the analytical and numerical approximation of invariant manifolds. In D. Benest and C. Froeschl´e, editors, Les M´ethodes Modernes de la M´ecanique C´eleste (course given at Goutelas, France, ´ 1989), pages 285–329. Editions Fronti`eres, Paris, 1990.

[SM71]

C.L. Siegel and J. Moser. Lectures on celestial mechanics, volume 187 of Grundlehren Math. Wiss. SpringerVerlag, Berlin–Heidelberg, 1971.

[Sot79]

J. Sotomayor. Li¸c˜ oes de equa¸c˜ oes diferenciais ordin´ arias, volume 11 of Projeto Euclides. IMPA, Rio de Janeiro, 1979.

[Sze67]

V. Szebehely. Theory of orbits: the restricted problem of three bodies. Academic Press, New York, 1967.

[Wil36]

J. Williamson. On the algebraic problem concerning the normal forms of linear dynamical systems. Amer. J. Math., 58(1):141–163, 1936.