A Behavioral Characterization of Discrete Time Dynamical Systems over Directed Graphs

• Jonathan Ackerman ^[1] ; Kimberly Ayers ^[1] ; Eduardo J. Beltran ^[4] ; Joshua Bonet ^[4] ; Devin Lu ^[2] ; Thomas Rudelius ^[3]
  1. [1] Bowdoin College

     Bowdoin College

     Town of Brunswick, Estados Unidos

     
  2. [2] Stanford University

     Stanford University

     Estados Unidos

     
  3. [3] Cornell University

     Cornell University

     City of Ithaca, Estados Unidos

     
  4. [4] University of Puerto Rico (USA)

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 13, Nº 1, 2014, págs. 161-180
• Idioma: inglés
• DOI: 10.1007/s12346-014-0111-2
• Texto completo no disponible (Saber más ...)
• Resumen

  • Using a directed graph, a Markov chain can be treated as a dynamical system over a compact space of bi-infinite sequences, with a flow given by the left shift of a sequence. In this paper, we show that the Morse sets of the finest Morse decomposition on this space can be related to communicating classes of the directed graph by considering lifting the communicating classes to the shift space. Finally, we prove that the flow restricted to these Morse sets is chaotic.