We construct a Teichmüller curve uniformized by the Fuchsian triangle group ∆(m, n, ∞) for every m < n ≤ ∞. Our construction includes the Teichmüller curves constructed by Veech and Ward as special cases. The construction essentially relies on properties of hypergeometric differential operators. We interprete some of the so-called Lyapunov exponents of the Kontsevich–Zorich cocycle as normalize...

It has been claimed that Lyapunov exponents computed from electroencephalogram or electrocorticogram (ECoG) time series are useful for early prediction of epileptic seizures. We show, by utilizing a paradigmatic chaotic system, that there are two major obstacles that can fundamentally hinder the predictive power of Lyapunov exponents computed from time series: finite-time statistical fluctuatio...

Baraviera and Bonatti in [1] proved that it is possible to perturb, in the Ctopology, a volume-preserving and partial hyperbolic diffeomorphism in order to obtain a non-zero sum of all the Lyapunov exponents in the central direction. In this article we obtain the analogous result for volume-preserving flows. MSC 2000: primary 37D30, 37D25; secondary 37A99. keywords: Dominated splitting; volume-...

Motivated by their important role in smooth dynamical systems, Lyapunov exponents have been conceived decades ago as a means to study the stability of cellular automata (CAs). More precisely, they quantify their sensitive dependence on initial conditions. As a next step towards the establishment of a dynamical systems theory of CAs that is inspired by its analogue for smooth dynamical systems, ...

Abstract. We study a matrix-valued Schrödinger operator with random point interactions. We prove the absence of absolutely continuous spectrum for this operator by proving that away from a discrete set its Lyapunov exponents do not vanish. For this we use a criterion by Gol’dsheid and Margulis and we prove the Zariski denseness, in the symplectic group, of the group generated by the transfer ma...

The theory of Lyapunov exponents and methods from ergodic theory have been employed by several authors in order to study persistence properties of dynamical systems generated by ODEs or by maps. Here we derive sufficient conditions for uniform persistence, formulated in the language of Lyapunov exponents, for a large class of dissipative discrete-time dynamical systems on the positive orthant o...

In this article, different methods of computing Lyapunov exponents for continuous-time dynamical systems are briefly reviewed. The relative merits and demerits of these methods are pointed out. 1. Preliminaries The problem of detecting and quantifying chaos in a wide variety of systems is an ongoing and important activity. In this context, computing the spectrum of Lyapunov exponents has proven...

Numerical estimation of Lyapunov exponents in non-linear dynamical systems results in a very high computational cost. This is due to the large-scale computational cost of several Runge–Kutta problems that need to be calculated. In this work we introduce a parallel implementation based on MPI (Message Passing Interface) for the calculation of the Lyapunov exponents for a multidimensional dynamic...

Local Lyapunov exponents of the quasi-geostrophic ocean dynamics.

In a previous paper [6] we suggested a numerical method for computing all Lyapunov exponents of a dynamical system by spatial integration with respect to an ergodic measure. The method extended an earlier approach of Aston and Dellnitz [2] for the largest Lyapunov exponent by integrating the diagonal entries from the QR-decomposition of the Jacobian for an iterated map. In this paper we provide...