A Spectral Gap for a One-dimensional Lattice of Coupled Piecewise Expanding Interval Maps

  • G Keller
  • C Liverani
Part of the Lecture Notes in Physics book series (LNP, volume 671)


Abstract. We study one-dimensional lattices of weakly coupled piecewise expanding interval maps as dynamical systems. Since neither the local maps need to have full branches nor the coupling map needs to be a homeomorphism of the infinite dimensional state space, we cannot use symbolic dynamics or other techniques from statistical mechanics. Instead we prove that the transfer operator of the infinite dimensional system has a spectral gap on suitable Banach spaces generated by measures with marginals that have densities of bounded variation. This implies in particular exponential decay of correlations in time and space.


Invariant Measure Transfer Operator Bounded Variation Invariant Probability Measure Compact Embedding 
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Authors and Affiliations

  • G Keller
    • 1
  • C Liverani
    • 2
  1. 1.Mathematisches InstitutUniversität Erlangen-Nürnberg91054 ErlangenGermany
  2. 2.Dipartimento di MatematicaUniversità di Roma II (Tor Vergata)00133 RomaItaly

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