Computing simplest normal forms for the takens-bogdanov singularity

Qualitative Theory of Dynamical Systems

Volumn 3, Issue 2, 2002, Pages 377-435

  Algaba, Antonio ^a   Freire, Emilio ^b   Gamero, Estanislao ^b  

^a UNIVERSITY OF HUELVA   (Spain)

^b UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Simplest normal forms; Takens bogdanov singularity

Indexed keywords

EID: 84896693908     PISSN: 15755460     EISSN: 16623592     Source Type: Journal    
DOI: 10.1007/BF02969413     Document Type: Article

References (13)

1. A. Algaba, E. Freire, and E. Gamero, Hypernormal forms for equilibria of vector fields. Codimension one linear degeneracies, Rocky Mountain Journal of Mathematics 29 (1999), 13-45.
2. A. Baider and J.A. Sanders, Further reduction of the Takens-Bogdanov normal form, Journal of Differential Equations 99 (1992), 205-244.
3. G. Chen and J. Della Dora, An algorithm for computing a new normal form for dynamical systems, Journal of Symbolic Computation 29 (2000), 393-418.
4. S. N. Chow and J. K. Hale, Methods of Bifurcation Theory, Springer-Verlag, New York (1982)
5. R. Cushman and J. A. Sanders, Nilpotent normal forms and representation theory of sl(2, r), Contemporary Mathematics 56 (1986), 31-51.
6. C. Elphick, E. Tirapegui, M.E. Brachet, P. Coullet, and G. Iooss, A simple global characterization for normal forms of singular vector fields, Physica D 29 (1987), 95-127.
7. E. Gamero, E. Freire, and E. Ponce, On the normal forms for planar systems with nilpotent linear part, International Series of Numerical Mathematics 97 (1991), 123-127.
8. H. Kokubu, H. Oka, and D. Wang, Linear grading function and further reduction of normal forms, Journal of Differential Equations 132 (1996), 293-318.
9. F. Loray, Ŕeduction formelle des singularit́es cuspidales de champs de vecteurs analytiques, Journal of Differential Equations 158 (1999), 152-173.
10. E. Stŕozyna, and H. Zoladek, The analytic and formal normal form for the nilpotent singularity, Journal of Differential Equations, 179 (2002), 479-537.
11. S. Ushiki, Normal forms for singularities of vector fields, Japan Journal of Applied Mathematics, 1 (1984), 1-37.
12. D. Wang, J. Li, M. Huang, and Y. Jiang, Unique normal form of Bogdanov-Takens singularities, Journal of Differential Equations, 163 (2000), 223-238.
13. Y. Yuan and P. Yu, Computation of simplest normal forms of differential equations associated with a double-zero eigenvalue, International Journal of Bifurcation and Chaos, 11 (2001), 1307-1330.