We study discontinuity of the Lyapunov exponent. We construct a limit-periodic Schrödinger operator, of which the Lyapunov exponent has a positive measure set of discontinuities. We also show that the limit-periodic potentials, whose Lyapunov exponent is discontinuous, are dense in the space of limit-periodic potentials.

a long time ago, since the launch of the first artificial satellite in 1957, controling attitude of satellites has been considered by the designers and engineers of aerospace industry. considering the importance of this issue various methods of control in response to this need have been presented and analyzed until now. in this paper, we propose and analyze a three-axis optimal control on the s...

It is the aim of this paper to further the use of Lyapunov and local Lyapunov exponent methods for analyzing phenomena involving nonlinear vessel dynamics. Lyapunov exponents represent a means to measure the rate of convergence or divergence of nearby trajectories thus denoting chaos and possibly leading to the onset of conditions that produce capsize. The work developed here makes use of Lyapu...

We present a method of approximating the unique invariant measure and associated Lyapunov exponents of a random dynamical system deened by the iid composition of a family of maps in situations where only one Lyapunov exponent is observed. As a corollary, our construction also provides a method of estimating the top Lyapunov exponent of an iid random matrix product. We develop rigorous numerical...

abstract tax is one of the main sources of financing government budget. therefore, having a clear picture about the attainable amount of taxes are not only necessary for optimal allocation of scarce resources for tax collection, but also helps the government to develop precise tax collection programs .in this article, the structural features of the tax revenues series have first been examined i...

chaos theory discusses unstable and non-periodic behavior of non-linear fluctuating dynamicsystems. since evaporation level variations of lakes have a dynamic identity, chaos theory can have a uniquerole in collecting data of these variations. therefore it is an important and challenging problem in the field ofplanning and qualitative and quantitative management of urmia lake to verify whether ...

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 ...

We study the fiber Lyapunov exponents of step skew-product maps over a complete shift of N , N ≥ 2, symbols and with C1 diffeomorphisms of the circle as fiber maps. The systems we study are transitive and genuinely nonhyperbolic, exhibiting simultaneously ergodic measures with positive, negative, and zero exponents. We derive a multifractal analysis for the topological entropy of the level sets...