Abstract
The local bifurcation structure of a heteroclinic bifurcation which has been observed in the Lorenz equations is analyzed. The existence of a particular heteroclinic loop at one point in a two-dimensional parameter space (a “T point”) implies the existence of a line of heteroclinic loops and a logarithmic spiral of homoclinic orbits, as well as countably many other topologically more complicatedT points in a small neighborhood in parameter space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K. H. Alfsen and J. FrØyland,Phys. Scripta 31:15–20 (1985).
P. Glendinning,Chaos due to Nonlocal Effects, preprint (University of Warwick, 1986).
P. Glendinning and C. Sparrow,J. Stat. Phys. 35:645–897 (1984).
J. Guckenheimer and R. E. Williams,Math. I.H.E.S. 50:59–72 (1979).
E. N. Lorenz,J. Atmos. Sci. 20:130–141 (1963).
C. Sparrow, The Lorentz Equations: Bifurcations Chaos and Strange Attractors,Appl. Math. Sci. 41 (Springer-Verlag, New York, 1982).
C. Sparrow,Homoclinic Bifurcations in Finite-Dimensional Flows, preprint (Cambridge University, 1984).
C. Tresser,C. R. Acad. Sci. (Paris) Ser. I 296:729–732 (1983).
C. Tresser,Ann. l'I.H.P. 40:441–461 (1984).
R. F. Williams,Math. I.H.E.S. 50:73–100 (1979).
L. P. Sil'nikov,Sov. Math. Dokl. 6:163–166 (1965).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Glendinning, P., Sparrow, C. T-points: A codimension two heteroclinic bifurcation. J Stat Phys 43, 479–488 (1986). https://doi.org/10.1007/BF01020649
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01020649