# American Institute of Mathematical Sciences

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

 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.
Citation: Russell Johnson, Francesca Mantellini. A nonautonomous transcritical bifurcation problem with an application to quasi-periodic bubbles. Discrete & Continuous Dynamical Systems - A, 2003, 9 (1) : 209-224. doi: 10.3934/dcds.2003.9.209
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