Pseudo-normal form near saddle-center or saddle-focus equilibria

Journal of Differential Equations

Volumn 208, Issue 2 SPEC. ISS., 2005, Pages 312-343

  Delshams, Amadeu ^a   Lázaro, Jose Tomás ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Convergence of normal forms; Hamiltonian systems; Reversible systems

Indexed keywords

EID: 11144322363     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2004.04.007     Document Type: Article

References (17)

1. Arnol'd V.I. Chapitres supplémentaires de la théorie des équations différentielles ordinaries 1980 Éditions Mir Moscou
2. Bruno A.D. Analytic form of differential equations (I) Trans. Moscow Math. Soc. 25 1971 131-288
3. Bruno A.D. Local Methods in Nonlinear Differential Equations, Series in Soviet Mathematics 1989 Springer Berlin
4. DeLatte D. On normal forms in Hamiltonian dynamics, a new approach to some convergence questions Ergodic Theory Dyn. Systems 15 1995 49-66
5. Delshams A. Guillamon A. Lázaro J.T. A pseudo-normal form for planar vector fields Qual. Theory Dyn. Systems 3 1 2002 51-82
6. Delshams D. Gelfreich V. Jorba À. Seara T.M. Exponentially small splitting of separatrices under fast quasiperiodic forcing Comm. Math. Phys. 189 1997 35-71
7. Devaney R.L. Reversible diffeomorphism and flows Trans. Amer. Math. Soc. 218 1976 89-113
8. Gaeta G. Cicogna G. Symmetry and Perturbation Theory in Nonlinear Dynamics Lecture Notes in Physics Vol. M57 1999 Springer Berlin
9. Giorgilli A. Unstable equilibria of Hamiltonian systems Discrete Continuous Dyn. Systems 7 4 2001 855-871
10. Lombardi E. Oscillatory Integrals and Phenomena Beyond All Algebraic Orders Lecture Notes in Mathematics Vol. 1741 2000 Springer Berlin
11. Lyapunov A.M. The general problem of the stability of motion, Moscow, 1892. Problème général de la estabilité du mouvement Ann. Fac. Sci. Toulouse 9 2 1907 202-474
12. van der Meer J.C. Sanders J.A. Vanderbauwhede A. Hamiltonian structure of the reversible nonsemisimple 1:1 resonance Chossat P. Dynamics, Bifurcation and Symmetry 1994 221-240 Kluwer Netherlands
13. Moser J.K. The analytic invariants of an area-preserving mapping near a hyperbolic fixed point Comm. Pure Appl. Math. IX 1956 673-692
14. Moser J.K. On the generalization of a theorem of A. Liapounoff Comm. Pure Appl. Math. XI 1958 257-271
15. Roberts J.A.G. Capel H.W. Area preserving mappings that are not reversible Phys. Lett. A 162 1992 243-248
16. Sevryuk M.B. Reversible Systems Lecture Notes in Mathematics Vol. 1211 1986 Springer Berlin
17. Vanderbauwhede A. Local Bifurcation and Symmetry Research Notes in Mathematics Vol. 75 1982 Pitman London