Invariant measures and equilibrium states for some mappings which expand distances
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 Trans. Amer. Math. Soc. 236 (1978), 121153 Request permission
Abstract:
For a certain collection of transformations T we define a PerronFrobenius operator and prove a convergence theorem for the powers of the operator along the lines of the theorem D. Ruelle proved in his investigation of the equilibrium states of onedimensional lattice systems. We use the convergence theorem to study the existence and ergodic properties of equilibrium states for T and also to study the problem of invariant measures for T. Examples of the transformations T considered are expanding maps, transformations arising from fexpansions and shift systems.References

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Additional Information
 © Copyright 1978 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 236 (1978), 121153
 MSC: Primary 28A65; Secondary 58F15
 DOI: https://doi.org/10.1090/S00029947197804664931
 MathSciNet review: 0466493