Centre families in two-dimensional complex holomorphic dynamical systems
Publication
, Journal Article
Needham, DJ; McAllister, S
Published in: Proc. R. Soc. Lond. A, Math. Phys. Eng. Sci. (UK)
1998
We consider a two-dimensional complex holomorphic dynamical system. In particular, we use the singular point theory of C.H. Briot and J.C. Bouquet to establish the existence of complex holomorphic invariant manifolds of the system in the neighbourhood of an equilibrium point with two purely imaginary eigenvalues. Consequently, this enables us to establish the existence of isochronous centre families in the neighbourhood of the equilibrium point. The results are exhibited by application to the complex Takens-Bogdanov system
Duke Scholars
Published In
Proc. R. Soc. Lond. A, Math. Phys. Eng. Sci. (UK)
DOI
Publication Date
1998
Volume
454
Issue
1976
Start / End Page
2267 / 2278
Related Subject Headings
- 51 Physical sciences
- 49 Mathematical sciences
- 40 Engineering
- 09 Engineering
- 02 Physical Sciences
- 01 Mathematical Sciences
Citation
APA
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Needham, D. J., & McAllister, S. (1998). Centre families in two-dimensional complex holomorphic dynamical systems. Proc. R. Soc. Lond. A, Math. Phys. Eng. Sci. (UK), 454(1976), 2267–2278. https://doi.org/10.1098/rspa.1998.0258
Needham, D. J., and S. McAllister. “Centre families in two-dimensional complex holomorphic dynamical systems.” Proc. R. Soc. Lond. A, Math. Phys. Eng. Sci. (UK) 454, no. 1976 (1998): 2267–78. https://doi.org/10.1098/rspa.1998.0258.
Needham DJ, McAllister S. Centre families in two-dimensional complex holomorphic dynamical systems. Proc R Soc Lond A, Math Phys Eng Sci (UK). 1998;454(1976):2267–78.
Needham, D. J., and S. McAllister. “Centre families in two-dimensional complex holomorphic dynamical systems.” Proc. R. Soc. Lond. A, Math. Phys. Eng. Sci. (UK), vol. 454, no. 1976, 1998, pp. 2267–78. Manual, doi:10.1098/rspa.1998.0258.
Needham DJ, McAllister S. Centre families in two-dimensional complex holomorphic dynamical systems. Proc R Soc Lond A, Math Phys Eng Sci (UK). 1998;454(1976):2267–2278.
Published In
Proc. R. Soc. Lond. A, Math. Phys. Eng. Sci. (UK)
DOI
Publication Date
1998
Volume
454
Issue
1976
Start / End Page
2267 / 2278
Related Subject Headings
- 51 Physical sciences
- 49 Mathematical sciences
- 40 Engineering
- 09 Engineering
- 02 Physical Sciences
- 01 Mathematical Sciences