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Invariant measures for real analytic expanding maps
Author(s) -
Bandtlow Oscar F.,
Jenkinson Oliver
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm001
Subject(s) - compact space , mathematics , holomorphic function , bounded function , lebesgue measure , probability measure , invariant (physics) , pure mathematics , analytic function , lebesgue integration , invariant measure , formalism (music) , countable set , measure (data warehouse) , discrete mathematics , mathematical analysis , computer science , data mining , art , musical , visual arts , ergodic theory , mathematical physics
Let X be a compact connected subset of ℝ d with non‐empty interior, and T : X → X a real analytic full branch expanding map with countably many branches. Elements of a thermodynamic formalism for such systems are developed, including criteria for compactness of transfer operators acting on spaces of bounded holomorphic functions. In particular, a new sufficient condition for the existence of a T ‐invariant probability measure equivalent to Lebesgue measure is obtained.