We consider the orbits of particles with spin in the Schwarzschild spacetime. Using the PapapetrouDixon equations of motion for spinning particles, we solve for the orbits and focus on those that exhibit chaos using both Poincaré maps and Lyapunov exponents. In particular, we develop a method for comparing the Lyapunov exponents of chaotic orbits. We find chaotic orbits for smaller spin values ...

The scaling function of Lyapunov exponents for intermittent systems is full of particularities if compared with hyperbolic cases or the usual, nonhyperbolic, parabola. One particularity arises when this function is calculated from finite-time Lyapunov exponents: Different scaling properties with respect to the length of the finite-time chains emerge. As expected from random walk models, the sca...

We show that for many strata of Abelian differentials in low genus the sum of Lyapunov exponents for the Teichmüller geodesic flow is the same for all Teichmüller curves in that stratum, hence equal to the sum of Lyapunov exponents for the whole stratum. This behavior is due to the disjointness property of Teichmüller curves with various geometrically defined divisors on moduli spaces of curves.

Given any compact connected manifold M , we describe Copen sets of iterated functions systems (IFS’s) admitting fully-supported ergodic measures whose Lyapunov exponents alongM are all zero. Moreover, these measures are approximated by measures supported on periodic orbits. We also describe C-open sets of IFS’s admitting ergodic measures of positive entropy whose Lyapunov exponents along M are ...

We present a method to calculate Lyapunov exponents of rigid diatomic molecules in three dimensions ( 12N -dimensional phase space). The spectra of Lyapunov exponents are obtained for 32 rigid diatomic molecules interacting through the Weeks-Chandler-Anderson potential for various bond length and densities, and compared with those of Shin [Phys. Rev. E 64, 041106 (2001)]. Our algorithm is easy ...

We compute the Lyapunov exponent, generalized Lyapunov exponents and the diffusion constant for a Lorentz gas on a square lattice, thus having infinite horizon. Approximate zeta functions, written in terms of probabilities rather than periodic orbits, are used in order to avoid the convergence problems of cycle expansions. The emphasis is on the relation between the analytic structure of the ze...

The transport properties of the Ando model on square lattice are studied numerically for box distribution of the diagonal disorder. The statistical properties of the Lyapunov exponents and of the conductance are discussed. It is shown that the statistics of the Lyapunov exponents agrees with the random matrix theory not only in the metallic regime, but even at the critical point. That confirms ...

The natural occurrence of small scale structures and the extreme anisotropy in the evolution of a magnetic eld embedded in a conducting ow is interpreted in terms of the properties of the local Lyapunov exponents along the various local characteristic (un)stable directions for the Lagrangian ow trajectories. The local Lyapunov exponents and the characteristic directions are functions of Lagrang...

An algorithm for estimating Lyapunov exponents of an unknown dynamical system is designed. The algorithm estimates not only the largest but all Lyapunov exponents of the unknown system. The estimation is carried out by a multivariate feedforward network estimation technique. We focus our attention on deterministic as well as noisy system estimation. The performance of the algorithm is very sati...