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

Russell Johnson; Francesca Mantellini

doi:10.3934/dcds.2003.9.209

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2003, Volume 9, Issue 1: 209-224. Doi: 10.3934/dcds.2003.9.209

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

Russell Johnson^1, and
Francesca Mantellini²

1.
Dipartimento di Sistemi e Informatica, Università di Firenze, 50139 Firenze
2.
Dipartimento di Matematica "U. Dini", Università di Firenze, 50139 Firenze

Received: May 31, 2001

Revised: May 31, 2002

Published: December 2002

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Abstract

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.

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Mathematics Subject Classification: 34C29, 37B55, 37G35.

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