T-points: a codimension two heteroclinic bifurcation

The local bifurcation structure of a heteroclinic 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 heteroclinc loops an...

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Veröffentlicht in:	J. Stat. Phys.; (United States) 1986-05, Vol.43 (3-4), p.479-488
Hauptverfasser:	GLENDINNING, P, SPARROW, C
Format:	Artikel
Sprache:	eng
Schlagworte:	657003 - Theoretical & Mathematical Physics- Relativity & Gravitation CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Exact sciences and technology FIELD THEORIES GENERAL RELATIVITY THEORY Geometry, differential geometry, and topology INVARIANCE PRINCIPLES LORENTZ INVARIANCE LORENTZ TRANSFORMATIONS MAPPING MATHEMATICAL MANIFOLDS Mathematical methods in physics MATHEMATICS Physics RELATIVITY THEORY TOPOLOGICAL MAPPING TOPOLOGY TRAJECTORIES TRANSFORMATIONS TWO-DIMENSIONAL CALCULATIONS
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Beschreibung
Zusammenfassung:	The local bifurcation structure of a heteroclinic 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 heteroclinc loops and a logarithmic spiral of homoclinic orbits, as well as countably many other topologically more complicated T points in a small neigborhood in a parameter space.
ISSN:	0022-4715 1572-9613
DOI:	10.1007/BF01020649