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

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

scholarly journals Divergence points of self-similar measures satisfying the OSC

2011 ◽  
Vol 379 (2) ◽  
pp. 834-841 ◽  
Author(s):  
Jia-Qing Xiao ◽  
Min Wu ◽  
Fei Gao
Keyword(s):  
Divergence Points ◽  
Self Similar

scholarly journals Divergence point analyses of visual world data: applications to bilingual research

2020 ◽  
pp. 1-9
Author(s):  
Kate Stone ◽  
Sol Lago ◽  
Daniel J. Schad
Keyword(s):  
Confidence Interval ◽  
Eye Tracking ◽  
Language Processing ◽  
Multiple Comparisons ◽  
Individual Factors ◽  
Visual World ◽  
World Data ◽  
Divergence Point ◽  
L2 Processing ◽  
Divergence Points

Abstract Much work has shown that differences in the timecourse of language processing are central to comparing native (L1) and non-native (L2) speakers. However, estimating the onset of experimental effects in timecourse data presents several statistical problems including multiple comparisons and autocorrelation. We compare several approaches to tackling these problems and illustrate them using an L1-L2 visual world eye-tracking dataset. We then present a bootstrapping procedure that allows not only estimation of an effect onset, but also of a temporal confidence interval around this divergence point. We describe how divergence points can be used to demonstrate timecourse differences between speaker groups or between experimental manipulations, two important issues in evaluating L2 processing accounts. We discuss possible extensions of the bootstrapping procedure, including determining divergence points for individual speakers and correlating them with individual factors like L2 exposure and proficiency. Data and an analysis tutorial are available at https://osf.io/exbmk/.

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.

Thermodynamic geometry of charged dilaton black holes in AdS spaces

2016 ◽  
Vol 94 (10) ◽  
pp. 1045-1053 ◽  
Author(s):  
Ahmad Sheykhi ◽  
Seyed Hossein Hendi ◽  
Fatemeh Naeimipour ◽  
Shahram Panahiyan ◽  
Behzad Eslam Panah
Keyword(s):  
Black Holes ◽  
Ricci Scalar ◽  
Thermodynamic Quantities ◽  
Geometrical Approach ◽  
De Sitter ◽  
Ads Black Holes ◽  
Divergence Points ◽  
The Stability ◽  
Thermodynamical Behavior ◽  
Dilaton Black Holes

It was shown that with the combination of three Liouville-type dilaton potentials, one can derive dilaton black holes in the background of anti-de-Sitter (AdS) spaces. In this paper, we further extend the study on the dilaton AdS black holes by investigating their thermodynamic instability through a geometry approach. First, we review thermodynamic quantities of the solutions and check the validity of the first law of thermodynamics. Then, we investigate phase transitions and stability of the solutions. In particular, we disclose the effects of the dilaton field on the stability of the black holes. We also employ the geometrical approach toward thermodynamical behavior of the system and find that the divergencies in the Ricci scalar coincide with roots and divergencies in the heat capacity. We find that the behavior of the Ricci scalar around divergence points depends on the type of the phase transition.

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.

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