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

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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

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

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