Lyapunov Spectrum of Asymptotically Sub-additive Potentials

By De-Jun Feng, Wen Huang. 2009

155 citations recorded by the source corpus.

For general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov exponents, measure-theoretic entropies and topological pressures in this general situation. Most of our results are obtained without the assumption of the existence of unique equilibrium measures or the differentiability of pressure functions. Some examples are constructed to illustrate the irregularity and the complexity of multifractal behaviors in the sub-additive case and in the case that the entropy map is not upper-semi continuous.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/159db622b240c5a6b9d685f0a4d8cdb8f3bd9881

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Variational principle for weighted topological pressure (2014, unknown): “(3) in [16], if μ = ∫ E(X1,T1)m dτ(m) is the ergodic decomposition of an element μ in M(X1, T1), then hμ(T1) = ∫ E(X1,T1) hm(T1) dτ(m), Φ∗(μ) = ∫ E(X1,T1) Φ∗(m) dτ(m).”
Non-conformal Repellers and the Continuity of Pressure for Matrix Cocycles (2013, background): “y M(A,s) is rather natural. On one hand, it is closely linked to the Lyapunov exponent of an IID random matrix product (see, e.g. [5, Chapter V]), and to the Lyapunov spectrum of matrix products (cf. [23, 21]). On the other hand, the limit as s → 0 (which in the thermodynamic formalism is known as a”
Local Entropy Theory of a Random Dynamical System (2011, unknown): “ [75, Theorem 4.5] and [75, Theorem 6.4] from Theorem 10.2 and Corollary 10.3, respectively. As the argument is the same as that of Remark 7.3, we omit the details. We also remark that Feng and Huang [27] considered the topological pressure of limit sub-additive potentials and obtained [27, Theorem ”
Equilibrium states of the pressure function for products of matrices (2010, methodology): “Some applications were given in the multifractal analysis of the top Lyapunov exponents of matrix products [11, 6, 8] (see also [10]).”