@article{ASENS_2001_4_34_2_159_0, author = {Sauzin, David}, title = {A new method for measuring the splitting of invariant manifolds}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {159--221}, publisher = {Elsevier}, volume = {Ser. 4, 34}, number = {2}, year = {2001}, doi = {10.1016/s0012-9593(00)01063-6}, mrnumber = {1841877}, zbl = {0987.37061}, language = {en}, url = {https://www.numdam.org/articles/10.1016/s0012-9593(00)01063-6/} }
TY - JOUR AU - Sauzin, David TI - A new method for measuring the splitting of invariant manifolds JO - Annales scientifiques de l'École Normale Supérieure PY - 2001 SP - 159 EP - 221 VL - 34 IS - 2 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/s0012-9593(00)01063-6/ DO - 10.1016/s0012-9593(00)01063-6 LA - en ID - ASENS_2001_4_34_2_159_0 ER -
%0 Journal Article %A Sauzin, David %T A new method for measuring the splitting of invariant manifolds %J Annales scientifiques de l'École Normale Supérieure %D 2001 %P 159-221 %V 34 %N 2 %I Elsevier %U https://www.numdam.org/articles/10.1016/s0012-9593(00)01063-6/ %R 10.1016/s0012-9593(00)01063-6 %G en %F ASENS_2001_4_34_2_159_0
Sauzin, David. A new method for measuring the splitting of invariant manifolds. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 34 (2001) no. 2, pp. 159-221. doi : 10.1016/s0012-9593(00)01063-6. https://www.numdam.org/articles/10.1016/s0012-9593(00)01063-6/
[1] Instability of dynamical systems with many degrees of freedom, Dokl. Akad. Nauk SSSR 156 (1964) 9-12, (in Russian). [English translation: Soviet Math. Dokl. 5 (1964) 581-585]. | Zbl
,[2] Lectures on Morse theory, old and new, Bull. Amer. Math. Soc. 7 (2) (1982) 331-358. | MR | Zbl
,[3] Local Methods in Nonlinear Differential Equations, Springer-Verlag, Berlin, 1989. | MR | Zbl
,[4] Exponentially small splitting of separatrices under fast quasi-periodic forcing, Comm. Math. Phys. 189 (1997) 35-71. | MR | Zbl
, , , ,[5] Homoclinic orbits to invariant tori in Hamiltonian systems, in: , , , , (Eds.), Multiple-Time-Scale Dynamical Systems, IMA Vol. in Math. and its Appl., Springer-Verlag, Berlin, 1998. | MR | Zbl
, ,[6] An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum, Comm. Math. Phys. 150 (1992) 433-463. | MR | Zbl
, ,[7] Splitting of separatrices in Hamiltonian systems with one and half degrees of freedom, Math. Phys. Elec. J. 3 (1997), paper 4. | MR | Zbl
, ,[8] Six lectures on transseries, analysable functions and the constructive proof of Dulac's conjecture, in: (Ed.), Bifurcations and Periodic Orbits of Vector Fields, Kluwer Academic, Dordrecht, 1993, pp. 75-184. | MR | Zbl
,[9] Biasymptotic solutions of perturbed integrable Hamiltonian systems, Bol. Soc. Bras. Mat. 25 (1) (1994) 57-76. | MR | Zbl
,[10] Exponentially small splitting of separatrices for difference equations with small step size, J. Dynam. Control Syst. 2 (2) (1996) 193-238. | MR | Zbl
, ,[11] Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable systems. A review, Rev. Math. Phys. 6 (3) (1994) 343-411. | MR | Zbl
,[12] Melnikov's approximation dominance. Some examples, Rev. Math. Phys. 11 (4) (1999) 451-461. | MR | Zbl
, , ,[13] Melnikov method and exponentially small splitting of separatrices, Physica D 101 (1997) 227-248. | MR | Zbl
,[14] On the conservation of hyperbolic invariant tori for Hamiltonian systems, J. Differential Equations 15 (1974) 1-69. | MR | Zbl
,[15] Invariant Manifolds, Lect. Notes in Math., 583, Springer-Verlag, Berlin, 1977. | MR | Zbl
, , ,[16] Splitting of separatrices for the Chirikov's standard map, Preprint VINITI 6372-84, 1984, (in Russian). | MR | Zbl
,[17] Effective speed of Arnol'd diffusion and small denominators, Phys. Lett. A 143 (1990) 39-42. | MR
,[18] Canonical perturbation theory via simultaneous approximation, Russian Math. Surveys 47 (1992) 57-133. | MR | Zbl
,[19] Hamiltonian perturbation theory: periodic orbits, resonances and intermittency, Nonlinearity 6 (1993) 885-904. | MR | Zbl
,[20] Tores invariants à torsion évanescente dans les systèmes hamiltoniens proches de l'intégrable, C.R. Acad. Sci. Paris, Série I 327 (1998) 833-836. | MR | Zbl
,[21] On the splitting of the invariant manifolds in multidimensional near-integrable Hamiltonian systems, Prépublication 220 de l'Institut de mathématiques de Jussieu, 1999. | Zbl
, , ,[22] Les méthodes nouvelles de la mécanique céleste, Vol. 2, Gauthier-Villars, Paris, 1893. | JFM | Zbl
,[23] Invariant tori, effective stability and quasimodes with exponentially small error terms, Preprint, 1999. | Zbl
,[24] Nekhoroshev estimates for quasi-convex Hamiltonian sytems, Math. Z. 213 (1993) 187-216. | EuDML | MR | Zbl
,[25] Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems, Physica D 114 (1998) 3-80. | MR | Zbl
, ,[26] Résurgence paramétrique et exponentielle petitesse de l'écart des séparatrices du pendule rapidement forcé, Ann. Inst. Fourier 45 (1995) 453-511. | EuDML | Numdam | MR | Zbl
,[27] Averaging under fast quasiperiodic forcing, in: (Ed.), Hamiltonian Mechanics: Integrability and Chaotic Behaviour, NATO Adv. Sci. Inst. Ser. B Phys., 331, Plenum Press, New York, 1994, pp. 13-34. | MR
,[28] A mechanism for the destruction of resonance tori of Hamiltonian systems, Math. USSR-Sbornik 68 (1) (1991) 181-203. | MR | Zbl
,[29] Hyperbolic tori and asymptotic surfaces in Hamiltonian systems, Russian J. Math. Phys. 2 (1) (1994) 93-110. | MR | Zbl
,[30] Introduction to hyperbolic dynamics, in: , (Eds.), Real and Complex Dynamical Systems, NATO Adv. Sci. Inst. Ser. C Math. and Phys. Sciences, 464, Kluwer Academic, Dordrecht, 1995, pp. 265-291. | MR | Zbl
,- A numerical study of the scattering in the He-Cu model with a Morse potential: Parabolic manifolds and exponentially small phenomena, Communications in Nonlinear Science and Numerical Simulation, Volume 139 (2024), p. 108260 | DOI:10.1016/j.cnsns.2024.108260
- Splitting of Separatrices for Rapid Degenerate Perturbations of the Classical Pendulum, SIAM Journal on Applied Dynamical Systems, Volume 23 (2024) no. 2, p. 1159 | DOI:10.1137/23m1550992
- Breakdown of homoclinic orbits to L3 in the RPC3BP (I). Complex singularities and the inner equation, Advances in Mathematics, Volume 408 (2022), p. 108562 | DOI:10.1016/j.aim.2022.108562
- Exponentially Small Splitting of Separatrices Associated to 3D Whiskered Tori with Cubic Frequencies, Communications in Mathematical Physics, Volume 378 (2020) no. 3, p. 1931 | DOI:10.1007/s00220-020-03832-y
- Stationary Phase Methods and the Splitting of Separatrices, Communications in Mathematical Physics, Volume 368 (2019) no. 3, p. 1297 | DOI:10.1007/s00220-019-03364-0
- Breakdown of a 2D Heteroclinic Connection in the Hopf-Zero Singularity (I), Journal of Nonlinear Science, Volume 28 (2018) no. 5, p. 1551 | DOI:10.1007/s00332-018-9458-x
- Exponentially Small Splitting of Separatrices and Transversality Associated to Whiskered Tori with Quadratic Frequency Ratio, SIAM Journal on Applied Dynamical Systems, Volume 15 (2016) no. 2, p. 981 | DOI:10.1137/15m1032776
- Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies, Electronic Research Announcements in Mathematical Sciences, Volume 21 (2014) no. 0, p. 41 | DOI:10.3934/era.2014.21.41
- Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio, Regular and Chaotic Dynamics, Volume 19 (2014) no. 6, p. 663 | DOI:10.1134/s1560354714060057
- Splitting of separatrices in the resonances of nearly integrable Hamiltonian systems of one and a half degrees of freedom, Discrete Continuous Dynamical Systems - A, Volume 33 (2013) no. 7, p. 2829 | DOI:10.3934/dcds.2013.33.2829
- Transversality of homoclinic orbits to hyperbolic equilibria in a Hamiltonian system, via the Hamilton–Jacobi equation, Physica D: Nonlinear Phenomena, Volume 243 (2013) no. 1, p. 64 | DOI:10.1016/j.physd.2012.09.009
- Homoclinic Solutions to Infinity and Oscillatory Motions in the Restricted Planar Circular Three Body Problem, Progress and Challenges in Dynamical Systems, Volume 54 (2013), p. 265 | DOI:10.1007/978-3-642-38830-9_16
- Exponentially and non-exponentially small splitting of separatrices for the pendulum with a fast meromorphic perturbation, Nonlinearity, Volume 25 (2012) no. 5, p. 1367 | DOI:10.1088/0951-7715/25/5/1367
- Speed of Arnold diffusion for analytic Hamiltonian systems, Inventiones mathematicae, Volume 186 (2011) no. 2, p. 255 | DOI:10.1007/s00222-011-0319-6
- An expansion of the homoclinic splitting matrix for the rapidly, quasiperiodically, forced pendulum, Journal of Mathematical Physics, Volume 51 (2010) no. 7 | DOI:10.1063/1.3398483
- Exponentially Small Splitting for the Pendulum: A Classical Problem Revisited, Journal of Nonlinear Science, Volume 20 (2010) no. 5, p. 595 | DOI:10.1007/s00332-010-9068-8
- The inner equation for one and a half degrees of freedom rapidly forced Hamiltonian systems, Nonlinearity, Volume 19 (2006) no. 6, p. 1415 | DOI:10.1088/0951-7715/19/6/011
- Exponentially Small Splitting of Separatrices for Whiskered Tori in Hamiltonian Systems, Journal of Mathematical Sciences, Volume 128 (2005) no. 2, p. 2726 | DOI:10.1007/s10958-005-0224-x
Cité par 18 documents. Sources : Crossref