We consider products of a i.i.d. sequence in set $\{f_1,\ldots,f_m\}$ preserving orientation diffeomorphisms the circle. we can naturally associate Lyapunov exponent $\lambda$. Under few assumptions, it is known that $\lambda\leq 0$ and equality holds if only $f_1,\ldots,f_m$ are simultaneously conjugated to rotations. In this paper, state quantitative version fact case where $C^k$ perturbation...

We consider stochastic dynamical systems operating under synchronization constraints on system events. The system dynamics is represented by a linear vector equation in an idempotent semiring through second-order state transition matrices with both random and constant entries. As the performance measure of interest, the Lyapunov exponent defined as the asymptotic mean growth rate of the system ...

From a kinematical point of view, the geometrical information of hamiltonian chaos is given by the (un)stable directions, while the dynamical information is given by the Lyapunov exponents. The finite time Lyapunov exponents are of particular importance in physics. The spatial variations of the finite time Lyapunov exponent and its associated (un)stable direction are related. Both of them are f...

We consider the design criteria of a chemical mixing device based on a chaotic flow, with an emphasis on the steady-state devices. The merit of a reactor, defined as the Q-factor, is related to the physical dimension of the device and the molecular diffusivity of the reactants through the local Lyapunov exponents of the flow. The local Lyapunov exponent can be calculated for any given flow fiel...

Using a multi-scaled, chaotic flow known as the KS model of turbulence [7], we investigate the dependence of Lyapunov exponents on various characteristics of the flow. We show that the KS model yields a power law relation between the Reynolds number and the maximum Lyapunov exponent, which is similar to that for a turbulent flow with the same energy spectrum. Our results show that the Lyapunov ...

We investigate regularity functions corresponding to a fixed Lyapunov bundle E in the Oseledets multiplicative ergodic theorem for an ergodic flow or diffeomorphism. These functions measure the deviation of the growth in norm of the linearized system from constant exponential growth. In general, Oseledets regularity functions were only known to be Borel measurable. Our main result is that if E ...

We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in relatively high dimensions. The same technique is also extended for stabilizability of positive systems by evaluating a polytope concave Lyapunov function (“antinorm”...

The dependence of the Lyapunov exponent on the closeness parameter, ǫ, in tangent bifurcation systems is investigated. We study and illustrate two averaging procedures for defining Lyapunov exponents in such systems. First, we develop theoretical expressions for an isolated tangency channel in which the Lyapunov exponent is defined on single channel passes. Numerical simulations were done to co...