Horseshoes and the Conley index spectrum - II: the theorem is sharp

M. C. Carbinatto; K. Mischaikow

doi:10.3934/dcds.1999.5.599

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1999, Volume 5, Issue 3: 599-616. Doi: 10.3934/dcds.1999.5.599

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Horseshoes and the Conley index spectrum - II: the theorem is sharp

M. C. Carbinatto^1, and
K. Mischaikow^2,

1.
ICMC - USP - Caixa Postal 668, 13560-970 - São Carlos, SP
2.
Center for Dynamical Systems and Nonlinear Studies, School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332

Received: May 1997

Revised: March 1998

Published: July 1999

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Abstract

Recent work has shown that in the setting of continuous maps on a locally compact metric space the spectrum of the Conley index can be used to conclude that the dynamics of an invariant set is at least as complicated as that of full shift dynamics on two symbols, that is, a horseshoe. In this paper, one considers which spectra are possible and then produce examples which clearly delineate which spectral conditions do or do not allow one to conclude the existence of a horseshoe.

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Mathematics Subject Classification: 34C35, 54H20.

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