Symmetric and reversible families of vector fields near a partially hyperbolic singularity

Ergodic Theory and Dynamical Systems

Volumn 20, Issue 6, 2000, Pages 1627-1637

  Bonckaert, Patrick ^a  

^a HASSELT UNIVERSITY   (Belgium)

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EID: 0034356490     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385700000900     Document Type: Article

References (18)

1. 2 symmetry. J. Nonlinear Sci. 4 (1994), 195-219.
2. P. Bonckaert. On the continuous dependence of the smooth change of coordinates in parametrized normal form theorems. J. Diff. Eq. 106 (1993), 107-120.
3. P. Bonckaert. Partially hyperbolic fixed points with constraints. Trans. Amer. Math. Soc. 348 (1996), 997-1011.
4. P. Bonckaert. Conjugacy of vector fields respecting additional properties. J. Dynam. Control Syst. 3 (1997), 419-432.
5. H. Broer. Formal normal forms for vector fields and some consequences for bifurcations in the volume preserving case. Dynamical Systems and Turbulence (Warwick 1980) (Lecture Notes in Mathematics, 898). Springer, 1981.
6. A. R. Champneys and J. Härterich. Cascades of homoclinic orbits to a saddle-centre for reversible and perturbed Hamiltonian systems. Preprint, 1998.
7. S.-N. Chow, C. Li and D. Wang. Normal Forms and Bifurcations of Planar Vector Fields. Cambridge University Press, 1994.
8. G. Gaeta. Normal forms of reversible dynamicle systems. Int. J. Theor. Phys. 33 (1994), 1917-1928.
9. P. Hirschberg and E. Knobloch. Šil'nikov-hopf bifurcation. Physica D 62 (1993), 202-216.
10. A. J. Homburg, H. Kokubu and V. Naudot. Homoclinic-doubling cascades. Preprint, 1998.
11. J. S. Lamb. Local bifurcations in k-symmetric dynamical systems. Nonlinearity 9 (1996), 537-557.
12. C. Robinson. Dynamical Systems, Stability, Symbolic Dynamics and Chaos. CRC Press, Boca Raton, FL, 1995.
13. 3. J. Diff. Eq. 126 (1996), 1-47.
14. M. R. Rychlik. Lorenz attractors through Šil'nikov-type bifurcation. Part I. Ergod. Th. & Dynam. Sys. 10 (1990), 793-821.
15. V. S. Samovol. Equivalence of systems of differential equations in a neighbourhood of a singular point. Trans. Moscow Math. Soc., 1983, pp. 217-237.
16. S. Sternberg. On the structure of local homeomorphisms of euclidean n-space, ii. Amer. J. Math. 80 (1958), 623-631.
17. F. Takens. Partially hyperbolic fixed points. Topology 10 (1971), 133-147.
18. S. van Strien. Center manifolds are not C∞. Math. Z. 166 (1979), 143-145.