scholarly journals Conformal measures and the Dobrushin-Lanford-Ruelle equations

2021 ◽  
pp. 1
Author(s):  
Luísa Borsato ◽  
Sophie MacDonald
Keyword(s):  
Conformal Measures

scholarly journals Dynamical multifractal zeta-functions and fine multifractal spectra of graph-directed self-conformal constructions

2015 ◽  
Vol 36 (6) ◽  
pp. 1922-1971 ◽  
Author(s):  
V. MIJOVIĆ ◽  
L. OLSEN
Keyword(s):  
General Class ◽  
Zeta Functions ◽  
Continuous Functions ◽  
Precise Information ◽  
Multifractal Spectra ◽  
Conformal Measures

We introduce multifractal pressure and dynamical multifractal zeta-functions providing precise information of a very general class of multifractal spectra, including, for example, the fine multifractal spectra of graph-directed self-conformal measures and the fine multifractal spectra of ergodic Birkhoff averages of continuous functions on graph-directed self-conformal sets.

scholarly journals Conformal measures for meromorphic maps

2018 ◽  
Vol 43 ◽  
pp. 247-266
Author(s):  
Krzysztof Baranski ◽  
Boguslawa Karpinska ◽  
Anna Zdunik
Keyword(s):  
Conformal Measures ◽  
Meromorphic Maps

Divergence points of self-conformal measures

2019 ◽  
Vol 189 (4) ◽  
pp. 735-763
Author(s):  
Pei Wang ◽  
Yong Ji ◽  
Ercai Chen ◽  
Yaqing Zhang
Keyword(s):  
Divergence Points ◽  
Conformal Measures

Thermodynamic formalism for certain nonhyperbolic maps

1999 ◽  
Vol 19 (5) ◽  
pp. 1365-1378 ◽  
Author(s):  
MICHIKO YURI
Keyword(s):  
Number Theory ◽  
Gibbs Measure ◽  
Existence And Uniqueness ◽  
Thermodynamic Formalism ◽  
Periodic Points ◽  
Two Dimensional ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
Conformal Measures ◽  
One Dimensional Maps

We establish a generalized thermodynamic formalism for certain nonhyperbolic maps with countably many preimages. We study existence and uniqueness of conformal measures and statistical properties of the equilibrium states absolutely continuous with respect to the conformal measures. We will see that such measures are not Gibbs but satisfy a version of Gibbs property (weak Gibbs measure). We apply our results to a one-parameter family of one-dimensional maps and a two-dimensional nonconformal map related to number theory. Both of them admit indifferent periodic points.

Local dimension for piecewise monotonic maps on the interval

1995 ◽  
Vol 15 (6) ◽  
pp. 1119-1142 ◽  
Author(s):  
Franz Hofbauer
Keyword(s):  
Hausdorff Dimension ◽  
Invariant Measures ◽  
Positive Characteristic ◽  
Characteristic Exponent ◽  
Local Dimension ◽  
Pressure Function ◽  
Piecewise Monotonic ◽  
Almost Everywhere ◽  
Conformal Measures

AbstractThe local dimension of invariant and conformal measures for piecewise monotonic transformations on the interval is considered. For ergodic invariant measures m with positive characteristic exponent χm we show that the local dimension exists almost everywhere and equals hm/χm For certain conformal measures we show a relation between a pressure function and the Hausdorff dimension of sets, on which the local dimension is constant.

Conformal measures for multidimensional piecewise invertible maps

2001 ◽  
Vol 21 (04) ◽  
Author(s):  
JÉRÔME BUZZI ◽  
FRÉDÉRIC PACCAUT ◽  
BERNARD SCHMITT
Keyword(s):  
Conformal Measures

scholarly journals Dissipative conformal measures on locally compact spaces

2014 ◽  
Vol 36 (2) ◽  
pp. 649-670 ◽  
Author(s):  
KLAUS THOMSEN
Keyword(s):  
Operator Algebras ◽  
Sufficient Conditions ◽  
Locally Compact ◽  
Compact Spaces ◽  
Ruelle Operator ◽  
Conformal Measures ◽  
Continuous Potential ◽  
The One ◽  
Necessary And Sufficient ◽  
Uniformly Continuous

The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among other things, the method is used to give necessary and sufficient conditions for the existence of eigenmeasures for the dual Ruelle operator associated to a locally compact non-compact irreducible Markov shift equipped with a uniformly continuous potential function. As an application to operator algebras the results are used to determine for which ${\it\beta}$ there are gauge invariant ${\it\beta}$-KMS weights on a simple graph $C^{\ast }$-algebra when the one-parameter automorphism group is given by a uniformly continuous real-valued function on the path space of the graph.

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