Related papers: Lyapunov exponents in complex dynamics and potenti…
This is a chapter of an encyclopedia which does not have an abstract.
Nowadays there are a number of surveys and theoretical works devoted to the Lyapunov exponents and Lyapunov dimension, however most of them are devoted to infinite dimensional systems or rely on special ergodic properties of the system. At…
We claim that looking at probability distributions of \emph{finite time} largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of…
Starting from a hyperbolic toral automorphism, we obtain, for a small volume preserving perturbation, an exact and rigorous second order perturbation expansion of the Lyapunov exponents.
This is a supplement to the article "Markov Chain Monte Carlo Based on Deterministic Transformations" available at http://arxiv.org/abs/1106.5850
Consider a topologically exact $C^3$ interval map without non-flat critical points. Following the works we did in \cite{LiRiv12two}, we give two equivalent characterizations of hyperbolic H\"{o}lder continuous potential in terms of the…
We consider the top Lyapunov exponent associated to a dissipative linear evolution equation posed on a separable Hilbert or Banach space. In many applications in partial differential equations, such equations are often posed on a scale of…
The problem of evaluation of Lyapunov exponent in queueing network analysis is considered based on models and methods of idempotent algebra. General existence conditions for Lyapunov exponent to exist in generalized linear stochastic…
This paper ("Two-Level Chromophore and Irreversibility", which can be found at arXiv:0804.0086) has been withdrawn by the author due to too many errors and misleading statements. This paper has been superseded by Section 2.11 and Chapter 7…
In this paper, two types of Lyapunov exponents: random Lyapunov exponents and directional Lyapunov exponents, and the corresponding entropies: random entropy and directional entropy, are considered for smooth $\mathbb{Z}^k$-actions. The…
In this thesis I develop a variety of techniques to train, evaluate, and sample from intractable and high dimensional probabilistic models. Abstract exceeds arXiv space limitations -- see PDF.
The persistence theory has been employed by several authors in order to study persistence properties of dynamical systems generated by ordinary differential equations or maps across diverse disciplines. In this note, the author discusses a…
We study discontinuity of the Lyapunov exponent. We construct a limit-periodic Schr\"odinger operator, of which the Lyapunov exponent has a positive measure set of discontinuities. We also show that the limit-periodic potentials, whose…
This paper investigates the weighted-averaging dynamic for unconstrained and constrained consensus problems. Through the use of a suitably defined adjoint dynamic, quadratic Lyapunov comparison functions are constructed to analyze the…
The cloned dynamical system theory is introduced and the Lyapunov exponents of this system are qualitatively proven to be same as the original dynamical system. This property indicates that these two systems have the same error propagation…
The paper is mostly a survey on recent results in Diophantine approximation, with emphasis on properties of exponents measuring various notions of Diophantine <approximation.
We study Lyapunov exponents for flat bundles over hyperbolic curves defined via parallel transport over the geodesic flow. We consider them as invariants on the space of Hitchin representations and show that there is a gap between any two…
In this paper we analyze local structure of several chaotic attractors recently suggested in literature as pseudohyperbolic. The absence of tangencies and thus the presence of the pseudohyperbolicity is verified using the method of angles…
We consider the simple random walk in i.i.d. nonnegative potentials on the $d$-dimensional cubic lattice $\mathbb{Z}^d$ ($d \geq 1$). In this model, the so-called Lyapunov exponent describes the cost of traveling for the simple random walk…
In this paper, we consider a monic, centred, hyperbolic polynomial of degree $d \ge 2$, restricted on its Julia set and compute its Lyapunov exponents with respect to certain weighted Lyubich's measures. In particular, we show a certain…