Invariant equilibrium states and duality transformation for infinite systems

2008 ◽  
pp. 152-160
Keyword(s):  
Equilibrium States ◽  
Invariant Equilibrium ◽  
Duality Transformation ◽  
Infinite Systems

scholarly journals Ergodic properties of matrix equilibrium states

2017 ◽  
Vol 38 (6) ◽  
pp. 2295-2320 ◽  
Author(s):  
IAN D. MORRIS
Keyword(s):  
Equilibrium State ◽  
Lyapunov Exponents ◽  
Equilibrium States ◽  
Invariant Equilibrium ◽  
Sufficient Condition ◽  
Ergodic Properties ◽  
General Sufficient Condition ◽  
Algebraic Properties ◽  
Bernoulli Measure ◽  
Zero Entropy

Given a finite irreducible set of real$d\times d$matrices$A_{1},\ldots ,A_{M}$and a real parameter$s>0$, there exists a unique shift-invariant equilibrium state on$\{1,\ldots ,M\}^{\mathbb{N}}$associated to$(A_{1},\ldots ,A_{M},s)$. In this paper we characterize the ergodic properties of such equilibrium states in terms of the algebraic properties of the semigroup generated by the associated matrices. We completely characterize when the equilibrium state has zero entropy, when it gives distinct Lyapunov exponents to the natural cocycle generated by$A_{1},\ldots ,A_{M}$, and when it is a Bernoulli measure. We also give a general sufficient condition for the equilibrium state to be mixing, and give an example where the equilibrium state is ergodic but not totally ergodic. Connections with a class of measures investigated by Kusuoka are explored in an appendix.

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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