Multiple purpose algorithms for invariant manifolds

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

Volumn 10, Issue 1-3, 2003, Pages 331-344

  Broer, Henk ^a   Hagen, Aaron ^b   Vegter, Gert ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

^b UNIVERSITY OF TEXAS AT ARLINGTON   (United States)

Author keywords

Bifurcation theory; Chaotic dynamics; Computational geometry; Graph transform; Invariant manifolds; Normal hyperbolicity; Numerical continuation

Indexed keywords

EID: 4544241816     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (15)

1. H. W. Broer, A. Hagen and G. Vegter, Finite element algorithms for invariant manifolds, in preparation.
2. H. W. Broer, A. Hagen and G. Vegter, Finite element algorithms for invariant manifolds - the saddle case, in preparation.
3. H. W. Broer, H. M. Osinga and G. Vegter, Algorithms for computing normally hyperbolic invariant manifolds, Z. angew. Math. Phys., 48, (1997) 480-524.
4. n with applications to finite element methods, Arch. Rational Mech. Anal., 46, (1972) 177-199.
5. L. Dieci and J. Lorenz, Computation of invariant tori by the method of characteristics, SIAM J. Numer. Anal., 32, (1995) 1436-1474.
6. N. Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J., 21, (1971/1972) 193-226.
7. A. Hagen, Hyperbolic structures of time discretizations and the dependence on the time step, Ph.D. Thesis, University of Minnesota, 1996.
8. M. W. Hirsch, Differential Topology, Springer-Verlag, New York, 1994.
9. M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Springer-Verlag, New York, 1977.
10. Y. Kuznetsov, Elements of applied bifurcation theory, Springer-Verlag, New York, 1998.
11. J. Palis and F. Takens, Hyperbolicity & sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press, Cambridge, 1993.
12. D. Ruelle, Elements of differentiable dynamics and bifurcation theory, Academic Press, Boston, 1989.
13. A. Shil'nikov, G. Nicolis, and C. Nicolis, Bifurcation and predictability analysis of a low-order atmospheric circulation model, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 5, (1995) 1701-1711.
14. C. Sparrow, The Lorenz equations: bifurcations, chaos, and strange attractors, Springer-Verlag, New York, 1982.
15. S. Wiggins, Normally hyperbolic invariant manifolds in dynamical systems, Springer-Verlag, New York, 1994.