Equilibrium States and Hausdorff Measures for Interval Maps | Zendy

Hofbauer Franz | Zendy; Keller Gerhard | Zendy

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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].

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