The dichotomy of Hausdorff measures and equilibrium states for parabolic rational maps

1992 ◽  
pp. 90-113 ◽  
Author(s):  
Manfred Denker ◽  
Mariusz Urbański
Keyword(s):  
Equilibrium States ◽  
Rational Maps ◽  
Hausdorff Measures

Statistical properties of equilibrium states for rational maps

2000 ◽  
Vol 20 (5) ◽  
pp. 1371-1390 ◽  
Author(s):  
NICOLAI HAYDN
Keyword(s):  
Critical Points ◽  
Statistical Properties ◽  
Equilibrium States ◽  
Rational Maps ◽  
Hölder Continuous ◽  
Return Times

Equilibrium states of rational maps for Hölder continuous potentials are not $\phi$-mixing, mainly due to the presence of critical points. Here we prove that for disks the normalized return times of arbitrary orders are, in the limit, Poisson distributed as the radius of the disks go to zero. The return times are normalized by the measure of the disks. We also show that rational maps are weakly Bernoulli with respect to the partition given by Denker and Urbanski.

Ergodic theory of equilibrium states for rational maps

Nonlinearity ◽  
1991 ◽  
Vol 4 (1) ◽  
pp. 103-134 ◽  
Author(s):  
M Denker ◽  
M Urbanski
Keyword(s):  
Ergodic Theory ◽  
Equilibrium States ◽  
Rational Maps

Equilibrium States and Hausdorff Measures for Interval Maps

1993 ◽  
Vol 164 (1) ◽  
pp. 239-257 ◽  
Author(s):  
Franz Hofbauer ◽  
Gerhard Keller
Keyword(s):  
Equilibrium States ◽  
Hausdorff Measures ◽  
Interval Maps

Hausdorff measures on Julia sets of subexpanding rational maps

1991 ◽  
Vol 76 (1-2) ◽  
pp. 193-214 ◽  
Author(s):  
M. Denker ◽  
M. Urbański
Keyword(s):  
Julia Sets ◽  
Rational Maps ◽  
Hausdorff Measures

ON HAUSDORFF MEASURES AND SBR MEASURES FOR PARABOLIC RATIONAL MAPS

1999 ◽  
Vol 09 (09) ◽  
pp. 1763-1769
Author(s):  
M. DENKER ◽  
S. ROHDE
Keyword(s):  
Hausdorff Dimension ◽  
Julia Set ◽  
Rational Maps ◽  
Hausdorff Measures ◽  
Rational Map ◽  
Absolutely Continuous ◽  
Conformal Measure

If J is the Julia set of a parabolic rational map having Hausdorff dimension h<1, we show that Sullivan's h-conformal measure on J is either absolutely continuous or orthogonal with respect to the Hausdorff measures defined by the function [Formula: see text], according to whether τ>τ0 or τ<τ0 for some explicitly computable τ0>0.

scholarly journals The equilibrium states for semigroups of rational maps

2008 ◽  
Vol 156 (4) ◽  
pp. 371-390 ◽  
Author(s):  
Hiroki Sumi ◽  
Mariusz Urbański
Keyword(s):  
Equilibrium States ◽  
Rational Maps

Macroeconomic Equilibrium Theory in the Context of Methodological Problems of Contemporary Economic Science

2008 ◽  
pp. 77-88
Author(s):  
M. Likhachev
Keyword(s):  
Empirical Analysis ◽  
Equilibrium States ◽  
Equilibrium Theory ◽  
Economic Systems ◽  
Economic Science ◽  
The Real ◽  
Theoretical Status ◽  
Methodological Problems ◽  
Real Stability

The article is devoted to the analysis of methodological problems in using the conception of macroeconomic equilibrium in contemporary economics. The author considers theoretical status and relevance of equilibrium conception and discusses different areas and limits of applicability of the equilibrium theory. Special attention is paid to different epistemological criteria for this theory taking into account both empirical analysis of the real stability of economic systems and the problem of unobservability of equilibrium states.

Fulfillment of Arbitrary Movement Transfer Control between Equilibrium States for a Double Pendulum Robot

2011 ◽  
Vol 36 (12) ◽  
pp. 1720-1731 ◽  
Author(s):  
Zu-Shu LI ◽  
Yuan-Hong DAN ◽  
Xiao-Chuan ZHANG ◽  
Lin XIAO ◽  
Zhi TAN
Keyword(s):  
Equilibrium States ◽  
Double Pendulum
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