Homoclinic bifurcation to a transitive attractor of Lorenz type
- 1 November 1989
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 2 (4) , 495-518
- https://doi.org/10.1088/0951-7715/2/4/001
Abstract
The author proves that a cubic differential equation in three dimensions has a transitive attractor similar to that of the geometric model of the Lorenz equations. In fact, what is proved is that such an attractor results if a double homoclinic connection of a fixed point with a resonance condition among the eigenvalues is broken in a careful way.Keywords
This publication has 10 references indexed in Scilit:
- On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fieldsBulletin of the Brazilian Mathematical Society, New Series, 1986
- Generalized bounded variation and applications to piecewise monotonic transformationsProbability Theory and Related Fields, 1985
- Transitivity and invariant measures for the geometric model of the Lorenz equationsErgodic Theory and Dynamical Systems, 1984
- Hyperbolicity conditions for the Lorenz modelPhysica D: Nonlinear Phenomena, 1981
- The structure of Lorenz attractorsPublications mathématiques de l'IHÉS, 1979
- Structural stability of Lorenz attractorsPublications mathématiques de l'IHÉS, 1979
- Expanding attractorsPublications mathématiques de l'IHÉS, 1974
- Partially hyperbolic fixed pointsTopology, 1971
- One-dimensional non-wandering setsTopology, 1967
- Deterministic Nonperiodic FlowJournal of the Atmospheric Sciences, 1963