American Institute of Mathematical Sciences

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July  1999, 5(3): 599-616. doi: 10.3934/dcds.1999.5.599

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, Brazil
2. 

Center for Dynamical Systems and Nonlinear Studies, School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States

Received  May 1997 Revised  March 1998 Published  May 1999

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.
Keywords: symbolic dynamics., Horseshoes, Conley index theory, Conley index spectrum, isolating neighborhoods.
Mathematics Subject Classification: 34C35, 54H2.
Citation: M. C. Carbinatto, K. Mischaikow. Horseshoes and the Conley index spectrum - II: the theorem is sharp. Discrete and Continuous Dynamical Systems, 1999, 5 (3) : 599-616. doi: 10.3934/dcds.1999.5.599
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