In this paper we show some symmetry properties of Lyapunov exponents of a dynamical system when the linearized problem evolves on a quadratic group, X HX = H , with H orthogonal. It is well understood that in this case the exponents are symmetric with respect to the origin. Here, we give lower bounds on the number of Lyapunov exponents which are 0, and show that some Lyapunov exponents may have...

Lyapunov exponents of a hyperbolic ergodic measure are approximated by Lyapunov exponents of hyperbolic atomic measures on periodic orbits.

The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion ...