Invariant measures for general(ized) induced transformations
By Roland Zweimüller. 2005
74 citations recorded by the source corpus.
We show that the general(ized) induced transformation T τ derived from an ergodic measure preserving transformation T by means of an inducing time r has an invariant measure canonically related to that of the original system iff a suitable induced version of τ is integrable. Moreover, we prove an Abramov-type entropy formula.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ba6472683c34b496c150a48beb588ea5b5ac41ec
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In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- STATISTICAL PROPERTIES OF ONE-DIMENSIONAL MAPS WITH CRITICAL POINTS AND SINGULARITIES (2006, background): “This is based on some recent progress on the thermodynamic formalism for abstract countable shift spaces [9, 24, 32, 43, 45], recent results on the relation between invariant measures for the system and invariant measures for the Markov tower extension [54], and the application of these results to s”
- Nice Inducing Schemes and the Thermodynamics of Rational Maps (2008, background): “See the book [Rue04] for an introduction to the thermodynamic formalism and [PU02, Zin96 ] for an introduction in the case of rational maps.”
- Equilibrium measures for maps with inducing schemes (2006, background): “By [47] (see also [6] for related results), there is a measure i (μ) ∈M (F,W ) that is absolutely continuous with respect to μ and such that Qi (μ) < ∞ and L (i (μ)) = μ.”
- Expanding Measures (2008, unknown): “Differently of Zweimüller’s results [66], this characterization is given by a statistical condition, condition (7), not by the integrability of the induced time with respect to the reference measure (the one that we want to lift).”