Stability of elliptic fixed points of analytic area-preserving mappings under the Bruno condition

Ergodic Theory and Dynamical Systems

Volumn 22, Issue 5, 2002, Pages 1551-1573

  Rüssmann, Helmut ^a  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036802524     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385702000974     Document Type: Article

References (9)

1. A.D. Bruno. Analytic form of differential equations. Trans. Moscow Math. Soc. 25 (1971), 131-288; 26 (1972), 199-239.
2. A.D. Bruno. Analytic form of differential equations. Trans. Moscow Math. Soc. 25 (1971), 131-288; 26 (1972), 199-239.
3. C. Camacho, N.H. Kuiper and J. Palis. The topology of holomorphic flows with singularity. Inst. Hautes Etudes Sci. Publ. Math. 48 (1978), 5-38.
4. n near a fixed point. Proc. VIII Int. Conf. on Mathematics and Physics (Marseille 1986). World Scientific Publishing, Singapore, 1987, pp. 138-198.
5. M. Herman. Some open problems in dynamical systems. Proc. ICM Berlin, Vol. II, 1998, pp. 797-808.
6. H. Rüssmann. Über die Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung; Math. Ann. 169 (1967), 55-72.
7. H. Rüssmann. On the convergence of power series transformations of analytic mappings near a fixed point into a normal form. Preprint I.H.E.S. MF/7/178 (1977), 1-44.
8. C.L. Siegel and J.K. Moser. Lectures on Celestial Mechanics. Springer, Berlin, 1971.
9. E. Zehnder. A Simple Proof of a Generalization of a Theorem by C.L. Siegel (Lecture Notes in Mathematics, 597). Springer, Berlin, 1977, pp. 828-854.