American Institute of Mathematical Sciences

July  1998, 4(3): 559-580. doi: 10.3934/dcds.1998.4.559

Heteroclinic bifurcations of $\Omega$-stable vector fields on 3-manifolds

 1 Institut für Mathematik I, Freie Universität Berlin, Arnimallee 2-6, 14195 Berlin, Germany

Received  May 1997 Revised  February 1998 Published  April 1998

We study one parameter families of vector fields that are defined on three dimensional manifolds and whose nonwandering sets are structurally stable. As families, these families may not be structurally stable; heteroclinic bifurcations that give rise to moduli can occur. Some but not all moduli are related to the geometry of stable and unstable manifolds. We study a notion of stability, weaker then structural stability, in which geometry and dynamics on stable and unstable manifolds are reflected. We classify the families from the above mentioned class of families that are stable in this sense.
Citation: Ale Jan Homburg. Heteroclinic bifurcations of $\Omega$-stable vector fields on 3-manifolds. Discrete & Continuous Dynamical Systems - A, 1998, 4 (3) : 559-580. doi: 10.3934/dcds.1998.4.559
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