Stochastic stability of the topological pressure

This is a survey on recent developments concerning a thermodynamic formalism for almost additive sequences of functions. While the nonadditive thermodynamic formalism applies to much more general sequences, at the present stage of the theory there are no general results concerning, for example, a variational principle for the topological pressure or the existence of equilibrium or Gibbs measures (at least without further restrictive assumptions). On the other hand, in the case of almost additive sequences, it is possible to establish a variational principle and to discuss the existence and uniqueness of equilibrium and Gibbs measures, among several other results. After presenting in a self-contained manner the foundations of the theory, the survey includes the description of three applications of the almost additive thermodynamic formalism: a multifractal analysis of Lyapunov exponents for a class of nonconformal repellers; a conditional variational principle for limits of almost additive sequences; and the study of dimension spectra that consider simultaneously limits into the future and into the past.

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Stochastic stability and its application to the analysis of gene regulatory networks

2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) ◽

10.1109/cdc.2004.1428924 ◽

2004 ◽

Cited By ~ 4

Author(s):

H. El Samad ◽

M. Khammash

Keyword(s):

Gene Regulatory Networks ◽

Stochastic Stability ◽

Regulatory Networks ◽

Gene Regulatory

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Moment Lyapunov exponent and stochastic stability of binary airfoil under combined harmonic and Gaussian white noise excitation

Nonlinear Dynamics ◽

10.1007/s11071-017-3470-9 ◽

2017 ◽

Vol 89 (1) ◽

pp. 539-552 ◽

Cited By ~ 5

Author(s):

D. L. Hu ◽

X. B. Liu ◽

W. Chen

Keyword(s):

Lyapunov Exponent ◽

White Noise ◽

Stochastic Stability ◽

Gaussian White Noise ◽

White Noise Excitation ◽

Moment Lyapunov Exponent

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VARIATIONAL PRINCIPLE FOR SUBADDITIVE SEQUENCE OF POTENTIALS IN BUNDLE RANDOM DYNAMICAL SYSTEMS

Stochastics and Dynamics ◽

10.1142/s0219493709002634 ◽

2009 ◽

Vol 09 (02) ◽

pp. 205-215 ◽

Cited By ~ 2

Author(s):

XIANFENG MA ◽

ERCAI CHEN

Keyword(s):

Dynamical Systems ◽

Variational Principle ◽

Multifractal Analysis ◽

Weak Condition ◽

Random Dynamical Systems ◽

Topological Pressure ◽

Set Up

The topological pressure is defined for subadditive sequence of potentials in bundle random dynamical systems. A variational principle for the topological pressure is set up in a very weak condition. The result may have some applications in the study of multifractal analysis for random version of nonconformal dynamical systems.

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