Communications in Mathematical Physics

, Volume 139, Issue 3, pp 551–557 | Cite as

On the essential spectrum of the transfer operator for expanding markov maps

  • Pierre Collet
  • Stefano Isola


The essential spectrum of the transfer operator for expanding markov maps of the interval is studied in detail. To this end we construct explicityly an infinite set of eigenfunctions which allows us to prove that the essential spectrum inC k is a disk whose radius is related to the free energy of the Liapunov exponent.


Neural Network Free Energy Statistical Physic Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Pierre Collet
    • 1
  • Stefano Isola
    • 2
  1. 1.Centre de Physique Théorique de l'Ecole PolytechniquePalaiseau CédexFrance
  2. 2.Dipartimento di Matematica e FisicaUniversità di CamerinoCamerinoItaly

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