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

M. C. Carbinatto, K. Mischaikow

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)599-616
Number of pages18
JournalDiscrete and Continuous Dynamical Systems
Volume5
Issue number3
StatePublished - Jul 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Conley index spectrum
  • Conley index theory
  • Horseshoes
  • Isolating neighborhoods
  • Symbolic dynamics

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