A method for the explicit computation of the Lyapunov exponents of certain Markov processes is developed. Its utility is demonstrated by an application to two-dimensional random evolution differential equations. Our approach exploits the relation between the Lyapunov exponent and the p-moment Lyapunov exponents, as was first observed and studied by Arnold [1]. The p-moment Lyapunov exponent is ...

Abstract We outline the flexibility program in smooth dynamics, focusing on of Lyapunov exponents for volume-preserving diffeomorphisms. prove results Anosov diffeomorphisms admitting dominated splittings into one-dimensional bundles.

In this article, we consider chaotic behavior happened in nonsmooth dynamical systems. To quantify such a behavior, a computation of Lyapunov exponents for chaotic orbits of a given nonsmooth dynamical system is focused. The Lyapunov exponent is a very important concept in chaotic theory, because this quantity measures the sensitive dependence on initial conditions in dynamical systems. Therefo...

different discrete models of population dynamics of certain insects have been investigated under various feasible conditions within the framework of nonlinear dynamics. evolutionary phenomena are discussed through bifurcation analysis leading to chaos. some tools of nonlinear dynamics, such as lyapunov characteristic exponents (lce), lyapunov numbers, correlation dimension, etc. are calculated ...

methods in this research, we utilized the chaos theory and fractal analysis in the interpretation of breast tumors on dce-mri. this cross-sectional study was done at pardisnoor imaging center during years 2015 and 2016 in iran. our sample size was 18 mass lesions, which were randomly selected among patients with birad 3 and birad 4 classification by the expert radiologist. the analysis was perf...

1. Lyapunov Exponents for Differential Equations 2. Abstract Theory of Lyapunov Exponents 3. Regularity of Lyapunov Exponents Associated with Differential Equations 4. Lyapunov Stability Theory 5. The Oseledets Decomposition 6. Dynamical Systems with Nonzero Lyapunov Exponents. Multiplicative Ergodic Theorem 7. Nonuniform Hyperbolicity. Regular Sets 8. Examples of Nonuniformly Hyperbolic System...

Lyapunov exponents are an important concept to describe qualitative properties of dynamical systems. For instance, chaotic systems can be caracterized with the positivity of the largest Lyapunov exponent. In this paper, we use the Iwasawa decomposition of the semisimple Lie group Sp(n,R) and the enlargement of the phase space to give a theoretical computation of Lyapunov exponents of almost per...

It is shown that the multifractal property is shared by both Lyapunov exponents and dual Lyapunov exponents related to scaling functions of one-dimensional expanding folding maps. This reveals in a quantitative way the complexity of the dynamics determined by such maps. (c) 1999 American Institute of Physics.

Consider a C vector field together with an ergodic invariant probability that has l nonzero Lyapunov exponents. Using orthonormal moving frames along certain transitive orbits we construct a linear system of l differential equations which is a reduced form of Liao’s “standard system”. We show that the Lyapunov exponents of this linear system coincide with all the nonzero exponents of the given ...