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Equilibrium States and Hausdorff Measures for Interval Maps
Author(s) -
Hofbauer Franz,
Keller Gerhard
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19931640117
Subject(s) - mathematics , hausdorff space , schwarzian derivative , interval (graph theory) , bounded function , monotone polygon , class (philosophy) , hausdorff distance , piecewise , pure mathematics , bounded variation , discrete mathematics , combinatorics , mathematical analysis , geometry , artificial intelligence , computer science
For a class of piecewise monotone interval maps T (including unimodal maps with negative Schwarzian derivative) and real valued functions f of bounded variation we compare equilibrium states μ of f with Hausdorff measures v and give an integral test for the dichotomy μ ≪ v or μ ⊥ v . For certain classes of rational maps such a result was proved in [15] and [3].