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January  2003, 9(1): 209-224. doi: 10.3934/dcds.2003.9.209

A nonautonomous transcritical bifurcation problem with an application to quasi-periodic bubbles

Russell Johnson 1, and  Francesca Mantellini 2,

1. 

Dipartimento di Sistemi e Informatica, Università di Firenze, 50139 Firenze
2. 

Dipartimento di Matematica "U. Dini", Università di Firenze, 50139 Firenze, Italy

Received  June 2001 Revised  June 2002 Published  November 2002

We study the phenomenon of stability breakdown for non-autonomous differential equations whose time dependence is determined by a minimal, strictly ergodic flow. We find that, under appropriate assumptions, a new attractor may appear. More generally, almost automorphic minimal sets are found.
Keywords: parameter intermittence., almost automorphic minimal set, Averaging method, bifurcation.
Mathematics Subject Classification: 34C29, 37B55, 37G3.
Citation: Russell Johnson, Francesca Mantellini. A nonautonomous transcritical bifurcation problem with an application to quasi-periodic bubbles. Discrete & Continuous Dynamical Systems, 2003, 9 (1) : 209-224. doi: 10.3934/dcds.2003.9.209
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