Automated computation of robust normal forms of planar analytic vector fields

Discrete and Continuous Dynamical Systems - Series B

Volumn 12, Issue 4, 2009, Pages 769-782

  Johnson, Tomas ^b   Tucker, Warwick ^a  

^a UNIVERSITY OF BERGEN   (Norway)

^b UPPSALA UNIVERSITY   (Sweden)

Author keywords

Hyperbolic fixed points; Normal forms; Numerical integration

Indexed keywords

EID: 73649088661     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2009.12.769     Document Type: Article

References (15)

1. G. Alefeld and J. Herzberger, "Introduction to Interval Computations", Academic Press, New York, 1983.
2. F. Blomquist, W. Hofschuster and W. Krämer, Real and complex Taylor arithmetic in C-XSC, Preprint 2005/4, Universität Wuppertal, 2005 Available from http://www.math.uni-wuppertal.de/-xsc.
3. CXSC - C++ eXtension for Scientific Computation, version 2.2.3. Available from http://www.math.uni-wuppertal.de/-xsc.
4. A. Griewank, "Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation", SIAM Frontiers in Applied Mathematics, 19, Philadelphia, 2000.
5. R. Hammer, M. Hocks, U. Kulisch and D. Ratz, "C++ Toolbox for Verified Computing", Springer-Verlag, New York, 1995.
6. E. Hille, "Ordinary Differential Equations in the Complex Domain", Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1976, xi+484 PP
7. T. Johnson and W. Tucker, On a computer-aided approach to the computation of Abelian integrals, preprint arXiv:0809.2867.
8. R. E. Moore, "Interval Analysis", Prentice-Hall, Englewood Cliffs, New Jersey, 1966.
9. R. E. Moore, "Methods and Applications of Interval Analysis", SIAM Studies in Applied Mathematics, Philadelphia, 1979.
10. A. Neumaier, "Interval Methods for Systems of Equations", Encyclopedia of Mathematics and its Applications 37, Cambridge Univ. Press, Cambridge, 1990
11. R. Roussarie, "Bifurcation of Planar Vector Fields and Hilbert's Sixteenth Problem", Progress in Mathematics, 164, Birkhauser Verlag, Basel, 1998.
12. C. L. Siegel, Über die Normalform analytischer Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl. Math.-Phys.-Chem. Abt., 1952 (1952), 21-30.
13. C. L. Siegel and J. K. Moser, "Lectures on Celestial Mechanics", Translation by Charles I. Kalme. Die Grundlehren der mathematischen Wissenschaften, Band 187. Springer-Verlag, New York-Heidelberg, 1971, xii+290 pp
14. W. Tucker, A rigorous ODE solver and Smale's 14th problem, Found. Comput. Math., 2 (2002), 53-117.
15. W. Tucker, Robust normal forms for saddles of analytic vector fields, Nonlinearity, 17 (2004), 1965-1983