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Title: Systoles in discrete dynamical systems
Authors: Fernandes, Sara
Grácio, Clara
Ramos, Carlos
Keywords: Iterated interval maps
Topological invariants
Topological Markov chains
Issue Date: 2013
Publisher: Elsevier
Citation: Fernandes S., Grácio C., Ramos C., Systoles in discrete dynamical systems, Journal of Geometry and Physics 63 (2013) 129–139
Abstract: The fruitful relationship between Geometry and Graph Theory has been explored by several authors benefiting also the Theory of discrete dynamical systems seen as Markov chains in graphs. In this work we will further explore the relation between these areas, giving a geo- metrical interpretation of notions from dynamical systems. In particular, we relate the topological entropy with the systole, here defined in the context of discrete dynamical systems. We show that for continuous interval maps the systole is trivial; however, for the class of interval maps with one discontinuity point the systole acquires relevance from the point of view of the dynamical behavior. Moreover, we define the geodesic length spectrum associated to a Markov interval map and we compute the referred spectrum in several examples.
Type: article
Appears in Collections:CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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